Pound meat between waxed paper until 1/8" thick. Combine next four ingredients. Coat veal in mixture; shake off excess and set aside. Preheat oven to 300 degrees F. In a large skillet, heat 5 tablespoons butter and the oil over moderately high heat.
Saute' half of veal at a time until lightly browned, 2 to 3 minutes on each side. Remove to a warm platter. Add vermouth to skillet and boil, scraping up browned bits, until liquid is reduced by half. Add stock and 3 tablespoons lemon juice, stirring well. Add parsley. Remove from heat. Sprinkle avocado with 1 tablespoon of lemon juice. Bake in small ovenproof dish 5 minutes.
Meanwhile, boil sauce in skillet until slightly reduced, about 2 minutes. Lower heat and whisk in remaining butter, a teaspoonful at a time, until sauce is slightly thickened. Place veal scallops on a warm platter and surround with avocado slices. Pour sauce over and serve at once.
Serves 6 to 8