Remove breast and back bones from quail; set quail aside.
Sauté onion in a nonstick skillet over low heat 10 minutes or until browned; add sugar and mushrooms, and sauté until tender. Stir in vinegar and next 4 ingredients. Spoon into quail cavities, and secure with wooden picks. Tuck wings under, and place, breast side up, in a buttered 2-quart baking dish. Brush with melted butter.
Bake at 350° for 20 minutes or until done. Serve over a bed of White Bean Ragout; drizzle evenly with Maple Brown Sauce.