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.
Heat 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.