Notice how dogs enjoy gnawing on bones? Ever been to a restaurant where they serve bone marrow?
Boiling bones in water draws flavor out of them. Most canned broth and stock you buy--beef stock, chicken stock, etc--is just this--water boiled with bones for hours.
Most literature I've read suggests using raw bones, but some recipes call for roasted bones--the ones I've seen most often involve roasted veal bones.
I've also made stock from roasted chicken bones. The stock does still take on flavor. It's easier to get good flavor from unused bones, though.
Additionally, I've found another pitfall. I've tried to make stock from the leftover bones of bbq'd ribs. This was not a good idea. The broth had a savory flavor, as intended. Unfortunately it also had the background taste of bbq sauce. Now, when I do make stocks, I'd consider using leftover bones, but
- there have to be enough bones leftover (otherwise I get very little stock for my time or it's weak on flavor)
- the bones can't be "tainted" by other flavors (like bbq sauce)
To answer your original question, try this:
- start with a pot of plain water
- put about 4 lb of bones in per gallon of water while it's still cold, add ~1 tsp of vinegar per gallon of water
- Once the water comes to a boil, lower the heat so that it's just simmering
- this keeps the stock from getting cloudy/white (which doesn't taste bad, just looks worse)
- leave boiling for about 6-8 hours, minimum. Longer is fine, but you won't get too much more at this point.
- turn off heat, allow stock to cool fully, strain it for the bones, refrigerate
- you can speed up this step by putting the pot in a sink full of cool water
- do NOT put a hot pot in your fridge. It will heat up the fridge significantly and just make the food in there go bad.
Use this to
- make soups
- make sauces (reduce it first)
- as a substitute for water in savory dish preparations (i.e. make rice with stock instead of water. Be creative here)
The main benefits here are flavor and nutrients, but I just do it for the flavor. Cutting bones up does improve the extraction process, but if the marrow is exposed already (most beef/veal bones will be) you're fine. If you save old bones, freeze them until you have enough. Don't bother trying to make stock with the bones from one chicken.
Ruhlman's ratios are very useful for baking, where the ingredients play an important role in the physical structure of the end result and a bad ratio can result in a bad cake (why didn't the bread rise?, etc.) They are OK for sauces to ensure a pleasant consistency (and partially because of the physical constraints of emulsified sauces), but much less important there. In fact, I generally make bechamel with twice as much milk as he says, and get a thinner bechamel which I find much nicer than his version. There is no structural problem with it (the way there would be if I tried to use twice the specified amount of milk in something like crepes).
In seasoning, there is no need to consult an external ratio at all. Sure, if you find exactly this ratio tasty, use it. But you can add any amount of fat and vinegar to your soup and get a good soup; your own taste preference is the only reliable guide there.
This said, it is rather unusual to add oil as a seasoning to a soup, and most Westerners don't add vinegar either. A soup is more nourishing when it has some fat, but it usually comes from the meat. It is also popular to sweat the onions (and sometimes some other long-cooking vegetables like carrots) in oil before adding the water, and the oil gets incorporated into the soup. The amount of oil in this case is judged by the onions: they should be evenly oiled, but not swim in a puddle of oil.
Some acidity usually improves a soup, and if you don't thicken with yoghurt, vinegar (or lemon juice) is a good choice. But most people who add it at all add pure vinegar when the soup is ready (to the pot or individually to each plate), and generally just add a squirt, then taste, add again, etc., until it tastes good to them. There is no ratio to follow.
I don't know of a tradition to add vinaigrette instead of vinegar of this point, but preparations containing vinaigrette are possible. For example, the garlic for tripe soup can be held either in pure vinegar or in a vinaigrette (but this is less common), and it gets spooned together with its fluid into the soup. However, if you decide that you like to use vinaigrette as a seasoning, just go ahead.
There is no point of using emulsified vinaigrette for soup (the emulsion will break). If you want to avoid fat bubbles swimming on the soup, make a thickened soup, the flour should bind them. This assumes a "standard" soup, a cream soup should have no trouble absorbing a bit of oil.
There is no need to use vinaigrette instead of pepper (although again, you can do it if that is what tastes best to you). It is better to use both, because they enrich the taste of the soup in very different ways.
The same applies to any other seasoning: no need to use a ratio, go by your own taste. Use as much pepper and salt as you like, nobody can prescribe you to like it exactly 3:1.
As for the traditional use for vinaigrette, it is a basic salad sauce. It can be used as-is, or turned into one of countless variations (actually Ruhlman explains it and gives some interesting variants). But for salads, it is preferable to emulsify it (usually with mustard), else it wilts the leaves. There was a Food lab article on that, but Ruhlman doesn't mention it and gives almost all vinaigrette recipes without mustard (except for the classic one, which of course has it).
Best Answer
Cook on a lower heat, in a pan with a thicker base, to distribute the heat. Check every now and again, and add water if the soup has become too thick. Also, the occasional stir can only help.
Consider buying a slow cooker -- there are very cheap models that do the job well.