Melt butter in a large skillet over medium-high heat. Coat chicken breasts in flour, and place them in the skillet along with the garlic. Fry on both sides until browned. Pour in the beef consomme, and reduce heat to low. Cover and simmer for 45 minutes.
Preheat the oven to 300 degrees F (150 degrees C). Stir together the sour cream and Dijon mustard, stir into the skillet, and simmer for 10 minutes.
Remove the chicken breasts from the skillet, and place them in a shallow casserole dish. Stir sauce until smooth, and pour over chicken. Sprinkle Parmesan cheese over the top.
Bake for 10 minutes in the preheated oven, or until cheese is melted. Serve with your favorite flavored rice.