Preheat oven to 350 degrees Fahrenheit. Wash your wings and pat them dry with a paper towel, season with salt, pepper, garlic and basil, arrange in one layer across a baking dish and set aside.
Melt butter in a pan and add 1/2 of your chopped onions and 1/2 of your minced garlic. After 2 minutes, add mushroom stems plus 1/2 of your chopped mushrooms. Add the flour and stir well. Slowly add 1/2 cup of chicken broth, stirring as it thickens. Add another 1 1/2 cup of broth and the cup of cream (reserve a cup of broth for later), alternating in 1/2 cup increments, and stir as it thickens. Add salt and pepper to taste and remove from heat.
Coat your wings with 1/3 or so of the mushroom soup base, reserving the rest for later. Cover the wings with foil and bake in the oven for approximately 1 1/2 to 2 hours. When the wings appear to be browning, remove them from the oven and drain the turkey drippings, stirring them into your soup base. Add the remaining broth to your soup base and stir well. Put your remaining onion, garlic, carrots and celery in the baking dish with your wings, pour the soup over the top and bake uncovered for another 30 to 60 minutes, or until the meat separates from the bone easily (but is not falling off). Serve over rice or pasta, and enjoy!