Cut peppers in half through the stems. Remove seeds and membranes; discard.
Heat oil in a large skillet over medium-high. Add beef; cook, stirring to crumble, until mostly browned, about 6 minutes. Add onion and garlic; cook, stirring, until beef is cooked and onion is tender, about 4 minutes. Stir in next 6 ingredients. Cook, undisturbed, 1 minute. Remove from heat; cool 5 minutes.
Divide mixture evenly among bell pepper halves (about 1/2 cup each). Arrange in a 9- x 13-inch baking dish.To cook now: Preheat oven to 350°F. Bake 10 minutes. Sprinkle cheese on peppers; bake until heated through, 20 to 35 minutes. Sprinkle with oregano.To freeze for later: Wrap dish tightly in 2 layers of plastic wrap. Wrap in heavy-duty aluminum foil. Freeze up to 1 month.To thaw and cook: Thaw in refrigerator 24 hours. Preheat oven to 350°F; place unwrapped dish on counter while oven preheats. Bake 20 minutes. Sprinkle cheese on peppers; bake 25 to 30 minutes. Sprinkle with oregano.