In 10-inch skillet over medium heat, in 1 tablespoon hot butter or margarine, cook mushrooms and onion until tender and liquid is evaporated; cool slightly. Preheat oven to 425 degrees.
Sprinkle flavor enhancer over both sides of steaks. Cut thawed pastry into four portions. Place 1/4 of mushroom mixture in center of each portion of pastry. Spread 1/4 of liverwurst spread over one side of each steak.
Place steaks, liverwurst side down, over mushrooms; wrap pastry around meat. If necessary, trim excess pastry from ends; seal ends.
Place pastry-wrapped meat, seam sides down, in greased shallow baking pan. In cup, beat egg and water; brush pastry with beaten egg. If desired, re-roll any trimmings to make cutouts. Place cutouts on pastry-wrapped meat.
Brush again with egg. Bake uncovered for 15 minutes or until pastry is golden and meat is medium-rare. If desired, test doneness of meat by inserting an instant-read thermometer into pastry-wrapped meat. Thermometer will read 145 degrees for medium-rare.
Meanwhile, prepare sauce: In medium saucepan, combine broth, wine, chopped shallot and thyme; heat to boiling. Reduce heat; simmer uncovered 5 to 7 minutes until mixture is reduced to about 1 1/2 cups.
In small bowl, mix remaining 4 tablespoons butter, softened, and flour until mixture is smooth. Add to wine mixture; cook until thickened and bubbly. Simmer 1 minute, stirring constantly. Stir in parsley. Serve with beef.