How to know when a recipe shouldn't contain onion/garlic?

Bolognese is (to Italians) a specific dish with a precise ingredient list. You wouldn't put garlic in a chocolate cake, but that's because it probably wouldn't taste nice. Imagine a chocolate cake to which you added coffee. Some people might enjoy the cake, some might not, but assuming it was a cake and had plenty of cocoa and/or chocolate, nobody would say it wasn't a chocolate cake. Now imagine you made a Tarte Tatin but you used pineapples instead of apples and you added chocolate, too. Some people might say "this isn't really a Tarte Tatin" because you're not following the traditional recipe for that pie. That's how they are feeling about the Bolognese sauce.

I expect that to you "Bolognese" means a vague category of tomato-and-meat sauce for putting on pasta, and you figure you can put in whatever you like as long as you like it. The Italians aren't complaining because garlic ruins the taste, but because when the sauce has garlic in it, it's not really a Bolognese any more, just as a Tarte Tatin with chocolate and pineapple isn't really a Tarte Tatin any more.

So the literal answer to your question is: garlic and onions do not belong in any dish that has a capital letters name and a generally accepted traditional recipe for that dish, where that traditional recipe doesn't include garlic or onions. If the dish doesn't have that kind of name (eg beef stew, grilled steak, roast chicken) then you're free to put in anything you like. It's not a matter of "not needed" or not, but of following a particular recipe or not.

As for the Bolognese with garlic, you could call it precisely that. Or "tomato and meat sauce with garlic." I bet it was yummy.

The general category for vegetables/herbs (that are not leafy green herbs, or spices) added to a dish for flavor (rather than bulk/texture/nutrition) is "aromatics", and that describes what they are there for: Add some basic aroma to complete the flavor profile. Typically added early and sauteed or sweated with some kind of culinary fat present to bind the aroma to something that can carry it.

Commonly used: Alliums (onions, spring onions, leeks, garlic,....), celery, rhizomes (ginger, galangal, (finely cut) carrot ...), capsicums (chile peppers, (finely cut) bell peppers..) ... Arguably, one might include tomato concentrate given the way it is sometimes used.

Sometimes the aroma is used as is, sometimes it's augmented by treating the aromatics in a way that adds Maillard reaction products.

There is also some effect on taste, mostly sweet and bitter components.

Some categories where onion and garlic are not always suitable:

• Sweet dishes - there typically is no sauteing step involved, and vegetable flavors typically do not work too well here - also because there is too little salt to offset bitter elements introduced.

• Dishes made in any culinary tradition that does not approve of alliums, e.g. Jain food, or recipes where alternatives like asafoetida are supposed to take this role completely

• Food to be served to people who want to avoid smelling of garlic or onions, or who are allergic or intolerant to it

• Raw preparations, sometimes - raw onions and garlic are very spicy and pungent, and have an even higher risk of causing undesirable breath seasoning.

• Anything where the garlic would burn (though, of course, you can add a garlic preparation afterwards) - burnt garlic is a generally very undesirable flavor.

• Using "normal" onions in dishes calling for shallots and/or spring onions can have undesirable flavor and/or texture effects.

My 2 centesimi (italian for cents) from a very much biased perspective, i.e. trying to push my subjective point of view with supposedly objective criteria.

Sugo alla Bolognese, or ragù alla Bolognese is a sauce which is traditionally eaten with tagliatelle or, more generally, egg-based fresh pasta. It is supposed to have a 'rounded' and somewhat sweet taste, and that's also why usually you cook it for quite long, in order to sweeten the tomato taste. Garlic is quite sharp in flavor, which clashes with the rest of the flavors, while onion becomes sweet as you cook it, and that's why it's usually preferred.

I would also add a more generic aspect: of course when you cook you are free to experiment with whatever combinations you like, and if possible you can try different versions of the same dish and compare them. A cook however (usually) has the goal to please his guests/customers and may choose depending on what they may expect. Also, typically they would indicate whether the recipe is traditional or revisited, unless their name speaks for them.

I think @rackandboneman and the others did a great job the "why and when it is desirable" part of the questions. But the "technically what garlic and onion is adding to the flavour" has triggered my scientific curiosity, and I would like to share another perspective on that bit!

Onion and garlic are both members of the Allium family (together with many great ingredients like leeks, spring onions, chives, etc). What all members of this family have in common is the presence of sulfur-rich compounds. Loosely speaking, compounds containing sulfur are usually very smelly. Think about odorized natural gas, rotten eggs, match heads, vulcano smoke (?).

There are many sulfur-containing compounds in garlic. But alliin is probably the most distinctive one. Chopping the garlic triggers a reaction that converts alliin into allicin, responsible for the characteristic smell of garlic. Here lies one culinary lesson: if you want to optimise the strong raw garlic flavour, chop it and leave it to fully react before using in your preparation.

On the other hand, instead of alliin, onions contain isoallin, a compound with the same chemical formula but different bond structure. Again, when the onion is chopped a chain of reactions is triggered. What is very curious is that the subtle chemical. The distinctive subproduct of isoalliin decomposition is a volatile compound propanethial S-oxide (PSO) which is responsible for the crying effect in onions. Again, another lesson: the longer you leave the chopped onions standing, the stronger the crying power.

I find this story interesting but offers only an explanation of the difference between raw garlic and onion. Allicin and PSO are both unstable when cooked under heat. You still get notes of raw garlic in fried or baked garlic, and to a less extent from onions, but it is not the whole picture.

The first important process that happens when cooking has not much to do with sulfur. It is the Maillard reaction, which in short is the conversion of sugars into flavourful molecules that give the 'roasted', 'umami' and 'caramelized' feel typical from bread crust or pan-fried meat. Onions typically have 4% of their weight of sugars, and garlic about 1%. However, since onion is usually used in much more quantity than garlic in recipes, it is clearly a dominant source of sugar. But there are exceptions. Different from what one might expect, roasted garlic soup or garlic purée is not that pungent and has a surprisingly sweet taste.

Apart from Maillard reaction, it seems that PSO decomposes into 3-mercapto-2-methylpentan-1-ol (MMP) under slow and long cooking, a compound that tastes like meat broth.. Since garlic does not have isoalliin, MMP is not produced when garlic is cooked. Maybe this is one of the reasons why onion pairs better with meat ragù than garlic? Mystery!

I found this and this useful references when reading about garlic/onions chemistry!

I am Italian and my eyes are bleeding after reading a lot of comments.

First of all, a lot of Italians do put garlic in the tomato sauce, whatever the sauce may be ("tomato and tuna", "tomato and bacon", and most of all in "ragù" - which is a sauce made with tomato and minced meat). So, to answer your question, there are some recipes that ask for a more pungent taste (garlic) and some other that are better for a sweeter one (onion) - see @greedyscholars answer too - : for example I would never use garlic in the "amatriciana sauce", but since we are living in a free world, who am I to say that you are not allowed to do it? I mean, you want to put pineapple on pizza? Be my guest. At the very worst I won't eat it. Don't expect to go to Italy and find that one though :)

It's very funny, however, that they were talking about the Bolognese, which is not (and I can't stress the "not" enough) in its most famous ("spaghetti with meatballs") form an Italian dish.

Historically the Ragù from Bologna (that's the meaning of "bolognese") was a dish for poor people, since it "recycled" leftover meat. Garlic and onions were never hard to get ahold of, even for poor people. So I guess both could have been used, depending on what was available.

That being said, it's true, in Italian cookbooks you won't find mention of garlic (they use onion instead) in the traditional recipe.