Simmer mirlitons about 1 hour. Cut in half, remove seeds and carefully spoon out pulp, reserving shells. Chop pulp and add bread crumbs.
Saute onions and garlic in butter over medium heat about 5 minutes. Add shrimp. Stir in pulp, salt and pepper. Continue cooking for 5 minutes, stirring frequently. Cool. Add egg, parsley and thyme and mix thoroughly. Fill shells and sprinkle tops with buttered bread crumbs. Bake at 375 degrees for 25 minutes. Serves 8.