Heat oven to 400°F. Grease large cookie sheet with shortening. In 10-inch skillet, cook ground beef, onion and bell pepper over medium heat, stirring frequently, until beef is thoroughly cooked; drain. Stir in tomato sauce, mushrooms, salt, pepper, and oregano. Reduce heat to low; simmer uncovered while preparing biscuit dough.
Separate dough into 10 biscuits. On cookie sheet, press or roll biscuits in 14x10-inch rectangle. Spread beef mixture lengthwise over half of dough. Place cheese slices over beef mixture. Carefully fold dough over cheese to form long rectangle; press edges with fork to seal.
Bake 15 to 20 minutes or until golden brown. Cut into pieces to serve.