Preheat oven to 350 degrees F (175 degrees C). Grease a 2-quart casserole dish.
Sprinkle the chicken breasts with salt, pepper, and paprika. Melt butter in a large skillet and brown the chicken breasts well on both sides, about 5 minutes per side. Lay the chicken breasts into the bottom of the prepared casserole dish.
In a saucepan over medium-low heat, mix together the mushroom soup, milk, onion, processed cheese, Worcestershire sauce, and mushrooms. Allow the mixture to heat until the cheese melts, but do not boil. Stir to thoroughly combine; mix in the sour cream until smooth. Pour the sauce over the chicken breasts in the dish and cover with foil.
Bake in the preheated oven until the chicken is tender and the juices run clear, about 45 minutes. Uncover, baste with sauce, and bake 30 more minutes, basting occasionally.