Melt the butter in a large skillet over medium heat. Add the mushrooms and onions. Cook until the vegetables are tender and most of the liquid has evaporated, stirring occasionally.

Blend in the flour, thyme, lemon juice, and Worcestershire sauce. Cook for 2 minutes, stirring constantly. Season with salt and pepper. Cool completely.

Unfold the thawed pastry sheets. Spread half the mushroom mixture over each puff pastry sheet. Roll up each pastry sheet, starting at one of the short ends, just to the center of the sheet. Roll up the opposite short side to the center. Press together.

Place the rolls on an ungreased baking sheet. Chill, covered, for at least 1 hour or until firm. (The rolls may also be frozen at this point.)

When ready to bake, preheat oven to 350 °F.

Cut the pastry rolls crosswise into 1/4-inch slices. Place, cut sides down, on an ungreased baking sheet.

Combine the egg and water in a bowl. Brush over the tops of the slices.

Bake for 20 minutes or until brown. Serve warm.