Place peppers in a large pot. Cover peppers with water and sprinkle water with a few dashes of salt. Bring to a boil, then reduce heat to low and cover. Simmer for 5 minutes. Remove peppers with a slotted spoon, allowing any water in peppers to spill back into pot. Set peppers aside.
Preheat oven to 350° F.
Heat butter and oil in a large skillet over medium heat until butter melts. Add chopped pepper tops and onion then reduce heat to low-medium and sauté for about 5 minutes or until tender. Add tomatoes, tomato sauce, garlic, oregano, basil, 1 teaspoon of the salt and 1/4 teaspoon of the pepper. Stir to combine, then simmer for about 10 minutes, uncovered.
In a large mixing bowl, combine egg with remaining teaspoon of salt, remaining 1/4 teaspoon of pepper and Worcestershire sauce. Gently stir to combine, then add ground beef, cooked rice and 1 cup of the tomato mixture from skillet. Mix well to combine (mixing with hands works best). Stuff peppers with meat mixture and place in a casserole dish. Spoon remaining tomato mixture over tops of peppers.
Bake for 55-65 minutes, uncovered. About 5 minutes before peppers are done, top each pepper with shredded cheddar cheese and continue baking until cheese has melted. Serve immediately.