Preheat oven to 350°F.
Cut bell peppers in half lengthwise, discarding seeds and membranes. Place peppers, cut side up, in a microwave-safe 13x9-inch baking dish. Add 2 tablespoons of water to the dish. Lightly cover with parchment paper. Microwave until peppers begin to soften, about 3 minutes. Drain any excess liquid.*
Meanwhile, prepare the filling.
Heat 1 tablespoon of olive oil in a large skillet or Dutch oven over medium-high heat. Add the ground beef and onion; cook until the meat is no longer pink. Drain off fat. Stir in cooked rice, tomato sauce, Worcestershire sauce, Italian seasoning, sugar, garlic powder, onion powder, salt, and pepper. Add ½ cup of cheddar and ½ cup of Monterey Jack or mozzarella. Taste and season with additional salt and pepper, if necessary.
Season the inside of each pepper with salt and pepper. Stuff peppers with beef mixture and drizzle with 1 tablespoon of olive oil. Cover with foil.
Bake until tender and heated through, about 35 minutes. Uncover, sprinkle with remaining ½ cup of cheddar and remaining ½ cup of Monterey Jack or mozzarella. Bake, uncovered, until cheese melts, about 10 more minutes. Serve warm. Garnish with fresh parsley or basil.