Arrange oven rack in upper third of the oven. Preheat broiler. Line a baking sheet with foil.

Heat oil in a large skillet over medium-high heat. Add beef, oregano, and salt; cook, crumbling with a wooden spoon, until cooked through, 4 to 6 minutes. Add tomato sauce and cook until bubbling, 1 to 2 minutes.

Meanwhile, warm peppers and onions in a small skillet over medium heat, stirring often. (Alternatively, microwave for 1 minute to reheat.)

Lay rolls, split-side open, on the prepared baking sheet. Broil, rotating the pan as necessary, until just starting to brown and toast, 1 to 2 minutes. Remove from the oven.

Top toasted buns with the beef mixture, dividing evenly. Top with the peppers and onions and then cheese. Broil just until the cheese is melted, 30 seconds to 1 minute. Wrap each sub in foil until ready to eat. Serve hot.