Drizzle butter into a casserole dish. Season chicken with salt, pepper and 1 tablespoon garlic. Wrap chicken thighs in prosciutto and place in casserole dish. Sprinkle mushrooms and remaining garlic on top of chicken.
Bake in a preheated oven until juices run clear, about 1 hour. Remove chicken to a platter and cover with aluminium foil to keep warm.
Pour drippings from casserole into a frypan over medium-low heat. Whisk in wine and sour cream and cook until warmed through, about 5 to 7 minutes. Pour over chicken, and serve.