1. Rub the turkey leg and thigh (or legs) with a fairly generous amount of salt and pepper. If you can do this and let the turkey parts sit overnight in the refrigerator, they’ll be a lot more delicious.
2. To cook the turkey, heat the olive oil in a Dutch oven over medium-high heat. Add the turkey to the pot to brown them. It’s best to put them in the pot in a single layer and not move them until they’re well-browned on one side. Once browned, turn them over to brown the other sides. Don’t rush this step as browning the turkey gives it additional flavor. It may take up to 15 to 20 minutes.
3. Remove the turkey and place the pieces in a bowl. Drain any excess fat from the pot, then add the bacon, and stir until it’s just cooked, about a minute. (French bacon isn’t fatty but if your bacon throws off a lot of fat, you can drain that off as well.) Add the shallots and stir for another minute or two, until they’re translucent.
4. Add the wine to the pot and cook, scraping the bottom of the pot to release any delicious browned bits. Then add the turkey pieces, the water or stock, and the branches of thyme. Bring the liquid to a boil, then reduce the heat to a simmer, cover, and cook for 1 1/4 hours, turning the turkey over a few times during cooking, so they cook evenly.
5. Turn off the heat and remove the turkey pieces to a bowl or plate. When cool enough to handle, pull the meat off the bones and return it to the liquid in the pot. Bring the mixture back to a simmer and let it cook to reduce the sauce until it’s thicker, richer in color, and in flavor.
6. While the sauce is reducing, in a separate wide skillet, melt the butter over high heat. Add the mushrooms, season with a little salt and pepper, and continue to cook, stirring occasionally, until they are about three-quarters of the way cooked through. Add the garlic and minced thyme, and continue to cook until the mushrooms are browned and completely cooked through. Turn off the heat and add chopped parsley and a squeeze of fresh lemon juice.
7. When the sauce is reduced to your liking, scrape the mushrooms and any liquid into the pot with the turkey. Taste, and season with additional salt and pepper, and serve.