Crumble and cook beef in a 10 to 12 inch frying pan over medium heat until well browned, about 5 minutes. Remove ground beef to a bowl.
Sauté onion and mushrooms in remaining beef fat for about 10 minutes or until onion is soft. Add garlic and cook 1 minute more.
Stir in soy sauce, scraping to loosen brown bits.
Remove from heat and stir in ground beef, eggs and pepper. Cool.
On a lightly floured board, roll each shell out to a 6 to 7-inch circle. Spoon 1/6 (about 1/3 to 1/2 cup) of meat mixture onto center.
Moisten edges with egg white and with seam on top, pinch firmly to seal. Flute edge. Pierce tops in several places to allow steam to escape.
Set on ungreased baking sheet. If made ahead, cover and chill up to 8 hours.
Bake, uncovered, at 450 degrees for about 20 minutes or until golden. Serve warm.
Makes approximately 6 servings.
A slice of cheddar cheese may also be added to pastries.