Preheat oven to 425 F (220 C). Season beef fillets with salt and pepper. In a large skillet, melt butter over medium heat. Add the beff and cook for 3minutes on each side or until browned. Remove from the skillet and let them cool. Add the shallts and sliced mushrooms to the skillet. Saute for 5 minutes. Add the beef broth and Italian seasoning. Unfold a pastry sheet onto a slightly floured surface and roll out to a 12x12 inch square. Cut the sheet into 4 squares. Place a filllet in the center of each square, and top it with some of the mushroom mixture. Bring the opposite corners of each sheet over the fillet and press to seal. Place covered filet on a baking sheet and brush with egg white. Place baking sheet in the lowest rack in the oven and bake for 20 to 25 minutes or until a meat thermometer reads 160 F (70 C) and pastry is golden brown.