1. In a large mixing bowl, use your hands to lightly but thoroughly combine chicken, bread crumbs, parsley, onion, thyme, salt, pepper, Worcestershire, and egg white. Form into 4 patties, each about 1/2 inch thick. Spoon about 2 tablespoons of flour onto a small plate. Dredge patties in flour to coat lightly.
2. Heat butter and oil in a large frying pan over medium heat. Add patties and cook, turning once with a spatula, until browned outside and white throughout, 10 to 13 minutes. Remove patfies to a platter.
3. Add mushrooms to drippings in pan and cook over medium-high heat, stirring often, until softened, about 5 minute. Stir in remaining flour and cook, stirring, 1 minute. Pour in wine and broth and bring to a boil, stirring, until thickened, 2 to 3 minutes. Season with additional salt and pepper to taste. Spoon sauce and mushrooms over chicken patties and serve at once.