In a large cast-iron or other heavy skillet, cook beef and onion over medium heat until the meat is no longer pink, 3-5 minutes, breaking into crumbles. Drain. Stir in the pizza sauce, mushrooms, sugar and oregano; mix well. Spoon onto buns; sprinkle with mozzarella cheese. , Place on ungreased baking sheets. Broil 4 in. from the heat until cheese is melted, 2 minutes. , Freeze option: Place the split and toasted buns on a baking sheet. Spoon the meat mixture onto buns; freeze for 1 hour. Transfer to freezer-safe airtight containers.