One standard item in supermarkets and on the outdoor markets all year long in France is the turkey leg. And when I say "leg" I mean the thigh + the drunstick. These are inexpensive and delicious. I'm not sure how widely available they are in the U.S. as a fresh product. I think you can get frozen turkey breasts, smoked turkey wings, and things like that, but are the legs and thighs widely available? Maybe you can ask the supermarket butcher for the legs.
I like to cook them in the slow cooker on low for as long as 12 hours. The one pictured above and below was one of three that I put into our six-liter mijoteuse ("simmerer") and cooked overnight. I season the turkey lightly with bay leaves, an onion, paprika, black pepper, a pinch of cloves, and of course some white wine.
These would be good cooked in red wine too, I find myself thinking all of a sudden. Whatever you do, don't add too much liquid to the pot. Use half water and half wine. The turkey will make its own broth as it cooks slowly at low temperature. The leg & thigh section here was the one on top in the pot, so it wasn't completely covered by the broth even after the cooking was finished. The skin looks lacquered, and the meat isn't boiled but steamed.
When the turkey legs are well-cooked, take them out of the broth, let them cool until you can comfortably handle them, and pull the meat off the bones with your fingers. Dispose of the cartilage, veins, and lumps of fat, as well the tiny, thin bones you'll find in the drumstick meat. Surtout, save the broth. Imagine what a good dinde au vin rouge — a version of the classic French coq au vin — you could make quickly with the rich red-wine broth, these nuggets of tender turkey meat, smoked pork-belly lardons, and sautéed mushrooms. Serve with pasta, steamed or mashed potatoes, or a green vegetable like petits pois or haricots verts.