I'm the kind of cook who wings it a lot, mostly based on experience, and I'm really interested in understanding the properties of ingredients.
You can almost categorize cuisines by the thickening agents they use. I've got a mental list of thickening agent that work, though I usually rely on the standards:
White flour-butter roux for French dishes
Cornstarch for Asian dishes
Beurre manee for stews
Then there are the things for particular dishes:
Flour-oil brown roux for gumbo
Cooked, pureed rice for bisque
Butter for rich sauces
Here are some that are open for discussion:
Coleman's Dry Mustard--I've found this to be an amazing thickener. Does anyone use it as such and for what?
Stale bread--Thinking of Italian soups and English bread sauce. Anyone have any novel uses?
Eggs--Not very adventurous here, beyond blanquette de veau, English baked puddings, and Hollandaise. Ideas?
Potato starch--open to ideas on this.
Nonfat dry milk--seems like it would work for something?
Tomato paste--Is it just my imagination, or does it thicken beyond the obvious original pastiness?
Peanut butter--Now this definitely thinkings exponentially from its original pastiness.
Chickpea flour -- applications as a thickener?
Any others, and what do you do with them? I there any way to get the shiny gelatinous quality of a real demi-glace by using another ingredient?
I suspect there's a wealth of information to plunder here.