While you prepare the mushroom sauté (skip the deglazing), thaw one sheet of frozen puff pastry at room temperature until pliable, 30 to 45 minutes. Set the sauté aside to cool.
Position a rack in the center of the oven and heat the oven to 425°F. Lightly dust a work surface with flour. Unfold the pastry sheet and roll it into a rectangle that's about 10x15 inches and about 1/16 inch thick. Slide it onto a baking sheet lined with parchment. With the exception of about an inch border around the rec-tangle, prick the pastry all over with a fork. With a pastry brush, brush the beaten egg over the border (you won't need all of it). Bake until the pastry begins to puff and the surface feels dry, about 5 minutes.
Scatter the mushroom sauté onto the pastry, leaving the inch or so -border uncovered. Bake until the crust border is puffed and deeply golden brown, about 10 minutes. Scatter the cheese over the mushrooms and continue baking until the cheese melts, another 2 to 3 minutes. Let cool briefly on a rack before slicing and serving.
nutrition information (per serving):
based on eight servings;
Photo: Scott Phillips