What is the best way to turn soup into stew without using flour?

I wouldn't actually call a soup with thickened liquid "a stew", for me a stew is a cooked dish with very little liquid altogether, be it thick or thin.

Because of this, I would suggest a very simple solution: pass your soup through a colander, catching the liquid. Then return as much liquid as you like to your vegetables, to get your stew. Keep the rest of the liquid to use as stock for another dish, or to drink pure as broth (you may have to freeze it if you don't plan to cook with it soon).

The second workable solution is to add more vegetables, grains or noodles and cook it more, as one of Juhasz's suggestions, but it has two drawbacks. First, it contradicts your keto restriction, and second, you will likely overcook the original vegetables, if you used sensitive ones.

All other solutions, including the starch, will produce a thickened liquid, but not actually a stew-like dish.

Let's leave aside the question of what separates a soup from a stew (there's no real answer, only mostly arbitrary opinions - which seems to be a somewhat widely shared belief around here: https://cooking.stackexchange.com/a/20963/70120). It sounds to me like you have a dish with some liquid in it and you want to thicken it.

There are a number of ways that soups/stews are traditionally thickened. I'd break them into four or six categories depending on how you want to count:

• Add starchy paste: this is the method you've already found, adding slurry made from flour and water. If you have a problem with wheat in particular, you could use corn starch, potato starch, etc. instead.

• Add a starchy ingredient and cook it: a similar idea, but rather than adding a slurry of flour/starch and water, you add some starchy food like noodles, bread, or potatoes. If you cook these starchy foods in the liquid for long enough, the starch will leech out of the potato/noodle/bread and into the liquid, having much the same effect as the first method. You can speed up this process by adding smaller particles, for example, shredded potatoes, or bread crumbs.

• Add gelatin: this is not much different than adding starch, except that you usually don't need to make a slurry, you can add the gelatin directly and it may have a lesser effect on the flavor. I'm including in this category thickeners like xanthan gum, or pectin, or other vegan alternatives to gelatin.

• Add a gelatin-containing ingredient and cook it: rather than adding gelatin directly, you can add an ingredient with gelatin in it. The most obvious choice here is bones. There's collagen in animal bones, as well as in skin and connective tissue (like you'd find in a tough cut of meat) and when you boil them (especially in something acidic) you'll get gelatin.

• Add cream: cream itself isn't much thicker than water, but the fat in the cream can make the soup/stew feel, well, creamier and less watery. Other milky ingredients can be used, including thicker ones like sour cream or yogurt. Generally speaking, the thicker the milky ingredient, the thicker the soup/stew, but if you add sour cream and then cook for a long time, it probably won't seem much thicker than it would have with milk. When we add thick milk products like sour cream and yogurt, we typically add them right at the end.

• Blend the soup: rather than adding a thick or thickening ingredient, you can add structure to the liquid by blending in whatever you were cooking in the liquid. This is very common in French vegetable soups. Often only a portion of the soup is blended, so that you end up with a thicker liquid and some large pieces of vegetables and meat.

Add a can of chickpeas to the soup/stew and include some of the liquid (Aquafaba) from the tin. The Aquafaba is an excellent thickener, even by itself.

You can mix it with mashed potatoes or with mashed pumpkin or butternut. You can overcook rice to the point that it becomes a mushy paste and use that as a thickener. You can even take stale bread pulse it a couple of times in the blender and then add it. Pea protein is another option. Can of peas, drain the liquid, mash the peas, use as thickener.

Some other suggestions, appending the list given by Juhasz:

• Psyllum husks can be used as a thickener but they might not be easily available. They don't have any taste whatsoever. The upside is that they are mostly non-digestible fiber which should play nicely with your condition. The downside is that they have a slight laxative effect, so use with moderation
• The remains of pressed linseed ("Linseed cake") are a potent thickener with a slight oily aftertaste, well suited to stews and soups. Also mostly fiber and likely not an issue with your condition. Very hard to source locally unfortunately.
• Agar-Agar may be used in place of gelatine (as a vegan option). Mostly tasteless, but tends to solidify a bit too much. Should also not be an issue with your condition
• Obviously there are different other starches such as tapioka flour
• The leafy parts of spring onions have a slight gelatine effect too

To turn it into a stew I use a family recipe that starts out looking like soup: tomato juice, V8 juice, beef, carrots, celery, potatoes and let it cook. Near the end we add red wine and some tapioca beads. Not many beads or powder is needed and that brings it to a stew consistency in 15-30 minutes. Add some dumplings or rolls and done. I used to cook this for dozens of friends on my dorm floor in college.

Adding to many other fine suggestions:

Add (cooked, drained) beans or (cooked or dry) lentils. The small red lentils, in particular, do a great job of thickening a pot.

Seeing that there is also a list of gluten-free flours that you may want to experiment with.Comments by the OP mentions auto-immune disease which to me means gluten intolerance. You do get some gluten free flours that can be used as thickening agents

• Almond Flour

Almond flour is one of the most common grain- and gluten-free flours. It’s made from ground, blanched almonds, which means the skin has been removed.

• Buckwheat Flour

Buckwheat may contain the word “wheat,” but it is not a wheat grain and is gluten-free. It belongs to the family of pseudocereals, a group of grains that are eaten like cereals but don’t belong to the grass family.

• Sorghum Flour

Sorghum flour is made from an ancient cereal grain that has been grown for more than 5,000 years. The grain is naturally gluten-free and considered the fifth most important cereal grain in the world.

• Amaranth Flour

Like buckwheat, amaranth is considered a pseudocereal. It’s a group of more than 60 grains that were once considered a staple food in the Inca, Maya and Aztec civilizations.

Amaranth has an earthy, nutty flavor and tends to take on the flavor of other ingredients. It can replace 25% of wheat flour but should be combined with other flours when baking. The best use of this type of flour is for making tortillas, pie crusts and bread

• Teff Flour

Teff flour has traditionally been used to make injera, a fermented, sourdough-like Ethiopian bread. It’s now also used for other foods like pancakes, cereals, breads and snacks. It can be substituted for 25–50% of wheat or all-purpose flour.

• Arrowroot Flour

Arrowroot flour is a less common gluten- and grain-free powder. It’s made from a starchy substance extracted from a tropical plant known as Maranta arundinacea.

• Brown Rice Flour

Brown rice flour is made from ground brown rice. It’s considered a whole-grain flour and contains the bran, germ and endosperm.

It has a nutty flavor and can be used to make a roux, thicken sauces or prepare breaded foods, such as fish and chicken. Brown rice flour is often used to make noodles and can be combined with other gluten-free flours for bread, cookie and cake recipes.

• Oat Flour

Oat flour is made by grinding whole-grain oats. It gives baked goods more flavor than all-purpose flour and results in a chewier, crumblier texture.

Baking with oat flour will likely make your end product more moist. Due to its lack of gluten, some ingredients will need to be adjusted to create light and fluffy baked goods.

• Corn Flour

Corn flour is a very finely ground version of cornmeal. Cornmeal is made from the whole kernel, including the bran, germ and endosperm.

It’s commonly used as a thickener for liquids and can be used to make tortillas and breads.

Corn flour comes in white and yellow varieties and can be combined with other gluten-free flours to make pizza crust.

• Chickpea Flour

Chickpeas are part of the legume family. Chickpea flour is made from dry chickpeas and is also known as garbanzo flour, gram flour and besan.

Chickpeas have a nutty taste and grainy texture and are popular in Middle Eastern and Indian cuisine. Chickpea flour is used to make falafel, hummus and the flatbread socca.

It’s a good source of fiber and plant-based protein. These nutrients work together to slow digestion, promote fullness and manage body weight

• Coconut Flour

Coconut flour is made from dried coconut meat and offers a mild coconut flavor.

Its light texture yields similar results to regular flour and is good for baking breads and desserts. Note that coconut flour absorbs a lot more water than regular or almond flour.

It’s high in the saturated fat lauric acid. This medium-chain triglyceride can provide energy for your body and may help lower “bad” LDL cholesterol in combination with the flour’s fiber content

• Tapioca Flour

Tapioca flour is made from the starchy liquid extracted from the South American cassava root.

This flour is used as a thickener in soups, sauces and pies and has no discernable flavor or taste. It can also be used in combination with other gluten-free flours in bread recipes.

Aside from carbohydrates, tapioca flour provides little nutritional value in the form of fiber, protein or micronutrients. In fact, it’s considered inferior to other whole-grain, gluten-free flours and often thought of as empty calories

• Cassava Flour

Cassava is a starchy root vegetable or tuber native to South America. It’s also known as yuca.

In contrast to tapioca flour, which is made from a starchy liquid extracted from the cassava root, cassava flour is made by grating and drying the whole root.

This flour is gluten-, grain- and nut-free.

It’s most similar to white flour and can easily be used in recipes calling for all-purpose flour. It has a neutral flavor and is easily digestible. It’s also lower in calories than coconut or almond flours.

• Tigernut Flour

Despite its name, tigernut flour is not made from nuts. Tigernuts are small root vegetables that grow in North Africa and the Mediterranean.

Tigernut flour has a sweet and nutty flavor that works well in baked goods. Its sweetness allows you to cut back on the sugar quantity in your recipe.

Note that it’s slightly coarser than white flour and likely results in products with more texture.

SOURCE