Saute shallots in butter in a large skillet over medium-high heat 2 minutes; add mushrooms and garlic. Cook 5 minutes or until liquid evaporates.
Add vermouth; cook until liquid evaporates.
Remove from heat; stir in thyme, 1/4 teaspoon salt, and 1/4 teaspoon pepper.
Sprinkle fillets with remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook fillets in a nonstick skillet over high heat 2 minutes on each side.
Roll each pastry shell into a 7-inch circle.
Spread about 1/4 cup mushroom mixture in center of each circle. Top with fillets. Wrap pastry over each fillet, tucking edges under fillet and pinching to seal.
Place, seam side down, on a rack in a broiler pan.
