Grease a 13x9x2-inch baking pan. Set aside.
In a food processor bowl or blender container, process or blend mushrooms until very finely chopped.
In a large skillet, melt butter. Add mushrooms, onion, Worcestershire sauce, and pepper. Cook over medium heat about 10 minutes or until most of the liquid has evaporated, stirring frequently. Remove from heat; cool.
Meanwhile, place each chicken breast half, boned side up, between two pieces of plastic wrap. Working from the center to the edge, pound lightly with the flat side of a mallet to form 1/8-inch-thick rectangle. Remove plastic wrap.
Cut pastry sheet into 4 rectangles. On lightly floured surface, roll out each rectangle into a 6-1/2 inch square.
Divide mushroom mixture among chicken breast pieces. Fold breasts over mushroom mixture to cover completely, tucking in edges. Place each chicken roll on a square of pastry. Brush edges of pastry with beaten egg. Fold in two sides of pastry over chicken, overlapping pastry; fold in remaining two sides. Seal edges. Tuck pastry ends under. Place, seam side down, in prepared pan. Brush pastry lightly with beaten egg.
Bake in a 400 degree F oven for 30 to 35 minutes or until rolls are golden brown.
Fifteen minutes before the chicken is done, prepare White Butter Sauce. Spoon onto warm serving plates. Place a chicken roll on each. Makes 4 servings.
In a small, heavy saucepan, cook wine and onion for 2 to 3 minutes or until reduce to about 1 tablespoon. Stir in whipping cream. Cook over medium heat for 20 minutes or until thickened, stirring often. Season to taste with salt and pepper.