Preheat oven to 375°F. Bring a large pot of water to a boil. Once boiling, add peppers and pepper tops and cook until tender, 6 to 7 minutes. Remove peppers from water and invert to drain fully.
Make filling: Warm olive oil in a large frying pan over medium-high heat. Add onion and cook, stirring occasionally, until translucent, about 4 minutes. Add carrot, celery and garlic and continue cooking until vegetables are just softened, 4 minutes longer. Add beef, salt and pepper and cook, breaking up large chunks, until meat is no longer pink, about 7 minutes. Add tomatoes and rice and cook 5 minutes longer. Stir in 3/4 cup cheese.
Fill peppers with meat mixture, dividing evenly. Sprinkle mixture with remaining cheese and top with pepper lid. Bake until cheese is melted and peppers are heated through, about 5 minutes. Serve hot.