Mix mustards. Heat 1 tablespoon oil. Add chopped onion and celery and saute until tender. Add vinegar and reduce by half. Stir in mustard mixture and brown stock. Cook 30 minutes. Add black pepper, dash salt and Worcestershire sauce. Strain into sauceboat. To make burgers, grind chicken and veal together. Stir in parsley, 1 1/2 teaspoons salt, white pepper, Worcestershire and hot pepper sauce. Soak bread in milk and add to meat mixture along with egg, mixing well. Heat 2 tablespoons oil, add sliced onion and cook until barely tender. Add mushrooms, bay leaf and thyme. Saute until liquid has evaporated. Remove bay leaf. Add mushroom mixture to meat mixture. Combine, stirring 2 to 4 minutes or combine in food processor until almost smooth. Form into patties and coat with bread crumbs. Melt butter in large skillet and add patties. Cook until browned on both sides, then remove from skillet. When ready to serve, place browned patties in baking pan and bake at 375F 10 minutes to crisp. Serve with mustard sauce.