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Heat the oven to 425°F.
Place the beef into a lightly greased roasting pan.
Season with the black pepper, if desired.
Roast for 30 minutes or until a meat thermometer reads 130°F.
Cover the pan and refrigerate for 1 hour.
Reheat the oven to 425°F.
Beat the egg and water in a small bowl with a fork or whisk.
Heat the butter in a 10-inch skillet over medium-high heat.
Add the mushrooms and onion and cook until the mushrooms are tender and all the liquid is evaporated, stirring often.
Unfold the pastry sheet on a lightly floured surface.
Roll the pastry sheet into a rectangle 4 inches longer and 6 inches wider than the beef.
Brush the pastry sheet with the egg mixture.
Spoon the mushroom mixture onto the pastry sheet to within 1-inch of the edges.
Place the beef in the center of the mushroom mixture.
Fold the pastry over the beef and press to seal.
Place seam-side down onto a baking sheet.
Tuck the ends under to seal.
Brush the pastry with the egg mixture.
Bake for 25 minutes or until the pastry is golden brown and a meat thermometer reads 140°F.