How to keep thick puréed sauces from separating into solids and liquids?

SAJ14SAJ has mentioned starch, but I wouldn't add any additional -- I'd just finish the pasta in the sauce.

Pull your pasta a minute or two early, let drain but do not rinse it, and add it to your sauce. The pasta will finish cooking in the sauce, absorbing some of the liquid. It will also release some of its starch into the liquid, helping to bind it.

If you can, reserve some of the pasta water to thin back out the sauce in case thickens too far. (A pyrex measuring cup works well for this, as you can just dip it into the hot water before you drain your pasta)

The core of this issue is: what makes a sauce seem integrated, as opposed to a bunch of liquid with stuff sitting in it.

While I am not sure there is any way to give a single scientific answer to what is essentially a question of perception, the common theme I find in all well integrated sauces is the viscosity of the liquid part of the sauce.

When the liquid phase is thick, it coats the solid chunks, and flows less freely, seeming to be a more integrated whole.

There are three common culinary methods that I can think of to create at thick, viscous liquid phase:

1. Reduce the sauce so that the natural solids and starches in the sauce make it thicker.

   This is often used with tomato sauces, or in other sauces and stews where some of the vegetables or legumes are pureed into the liquid phase.

   With this method, the cooking time helps reduce the liquids.

2. Thicken the sauce with colloidal binders, usually starch of some sort.

   This technique is very prevalent in gravies (using a roux, a beurre mannier, a flour starch slurry), or with corn starch, arrow root, and so on. The so-called modernist methods also favor agar agar or xantham gum from time to time.

   With this method, cooking time is also important. Each of the starch based binders (flour, cornstarch/cornflour, potato starch, arrow root) must be heated to a critical temperature in order to thicken fully, and to loose its raw taste. Continuing to cook for long periods will then begin to break down the starch, and the sauce will slowly thin, but this is not often observed in common cooking techniques.

3. Create an emulsion with fat that thickens the overall liquid.

   This is done in many French-technique pan sauces, by stirring in cold butter to finish. It is also the core technique in mayonnaise, and the Hollandaise/Bernaise family of sauces, and in many salad dressing type sauces.

   Heat management is very important in some of these sauces, as mismanagement can break the emulsion, but I will not address that further here, as I don't think this class was at the core of the original question.

Secondarily, having smaller, well cooked solid ingredients (for example, diced sauteed celery instead of large chunks of crunchy raw celery) in the sauce probably contributes to the perception of cohesion. This is usually a side effect of the entire recipe, so I won't address it further.

I use filler like corn or tapiaco starch for chili type sauces.

For gravy sauces, I find using mashed potatoes as filler effective too.

Maybe, I should try using sweet potatoes and/or yam too. I did once try mixing cottage cheese after the gravy was done. Which, I recall, was a disaster, both structurally and flavour-wise. O, maybe you could try apple-sauce?

I also find boiling egg plant/brinjal till the brinjal melts into the sauce helpful in holding the sauce/gravy together. I notice that many Indian gravies (aka curries) have mashed channa (chick pea gravy), melted brinjal and mashed potatoes as the "holding medium". Instead of pouring the sauce onto a naan/roti, I pour it onto my pasta.

But then, wouldn't people disdain me for contaminating an Italian concoction with Indian characteristics?

Chick pea gravies (aka hummus) basted with olive oil and garlic are also a very Mediterranean characteristic, which also seems to be a favourite component in both Arab and Israeli casual eating establishments. I don't know, but I think you have to add the vegetable sauce to the basted hummus rather than the other way round, to retain the characteristics of the hummus in a controllable manner - it's my hypothesis, because I've not seen any Israeli/Arab small-establishment chef/vendor (where they cook in front of you) dunking their medal-worthy hummus into vegetable sauce. But since none of them are looking, I am sure you could do it the other way round.

When I say basting, I recall they actually fry it on a pan/hot table-plate rather than basting in an oven.

I find solely using melted brinjal very helpful as a holding medium and does not alter the flavour of a gravy noticeably, except to contribute more towards its being a vegetable-based sauce. First, you need to acquire some familiarity with melting brinjals/egg plants into a gravy thro trial and error.

Oh BTW, that week-old precooked pot of cheap pasta (I bought 95ct a pack from Walmart) in the fridge, you could boil some with your sauce till the stale pasta melts into the sauce. Functions well as a binding agent - flavoour-wise, I don't know.