Stop! Drop that turkey carcass! Yes, I'm talking to you there, the one about to throw your leftover Thanksgiving turkey bones into a stockpot with some water and vegetables and simmer it all together to make stock.
I need to talk to you about what you're about to do. Don't worry; you're not doing anything wrong. In fact, you get bonus points for your resourcefulness—there's absolutely no reason all those bones shouldn't be put toward some homemade stock before they find their way to the trash can. But you can do it better. I know you just finished a marathon of Thanksgiving cooking, and the last thing you want is to complicate what is otherwise a relatively effortless task. With just a couple of extra steps, though, you can reap a much, much better reward. That reward is a rich and flavorful brown turkey stock, made from deeply roasted bones.
Here's the thing: It's pretty hard to convince most home cooks to make stock at all, even though it's an incredibly easy process and promises to deliver far better results than store-bought broth, at least in recipes in which the stock is a significant ingredient. On top of that, because home cooks have limited fridge and freezer space, it's not practical for most of us to keep multiple types of stock...in stock.
That's why I usually recommend making white chicken stock instead (i.e., a stock made by simmering raw chicken parts and vegetables in water). It has a deep flavor that still manages to be clean and neutral enough to make it the most versatile of all types of stock—it can work in the widest variety of recipes, from a rich and hearty beef stew to a light fish dish. There's no other stock, except maybe vegetable, that can switch-hit so well (and vegetable stock lacks gelatin, so it doesn't deliver the great body of a well-made meat stock).
The problem is that your turkey carcass has been cooked, so it won't deliver the clean, pure flavor of a white poultry stock made from raw meat and bones. But you also won't get a true brown stock out of it, since the bones were hiding under a cladding of moist meat while your bird was in the oven. As a result, their flavor will be more steamed than roasted. Simmer them as they are and you'll end up with a broth that's stranded in the murky no-man's-land between white and brown stock.
The solution, then, is to toss your turkey carcass in oil and throw it back in the oven until it's roasted more fully. This is going to give it a deeper, more complex flavor that you can then impart to the stock—the Maillard reaction's dark and savory signature.
And, as is the way with brown stocks, if you're going to roast the bones, you might as well go all in and brown the aromatic vegetables, like onion, carrot, and celery, too. You can do that in the oven, but I find it more efficient to brown them in batches in the stockpot while the bones are roasting.
One other hallmark of a brown stock is the inclusion of tomato, which is not used in a white stock. I like to add a couple of tablespoons of tomato paste to the pot once all the vegetables are browned, stirring it into the oil and cooking it for a minute or two to develop and darken its flavor.
Once that's done, just add your roasted bones to the pot, along with herbs like parsley, thyme, and bay leaf, and add enough water to just barely cover; a few black peppercorns tossed in won't hurt either.
Also, don't forget to use some water to deglaze the baking sheets you roasted the bones on: That's additional flavor you want to capture and add to your stock. Then gently simmer it for a few hours to extract as much flavor and gelatin from the bones and aromatics as possible. When strained and chilled, the stock should set like jelly, a sign you've done it right.
The resulting brown turkey stock will work anywhere a brown chicken stock would be a good choice, given their similar flavors. Where's that? Pretty much any dish that includes browning as a central part of the process. Think French onion soup with its darkly caramelized onions, most stews and braised meat dishes, and pan sauces that go with seared and roasted meats. It's not as versatile as a white stock, which can go into all of those dishes and more, but brown stock gives you the chance to double down on that deep roasted flavor when the situation calls for it.
Okay, you can pick that carcass back up—now that you know what to do with it.