Slice across the tops of the tomatoes and bell peppers to expose the interior of the vegetables. Reserve the tops to serve as 'hats' during the cooking process. Scoop out and discard any flesh and seeds from inside the tomatoes. Seed the peppers. Set the veggies aside.
In a large mixing bowl, combine ground beef, chopped onions, salt and pepper. Mix together thoroughly. Stuff each vegetable with ground beef mixture to the top and cover with their 'hats.' Arrange each vegetable in the bottom of a 5- to 6-quart pot or dutch oven in a concentric circle, very tightly together.
Pour fresh cold water over vegetables in the pot, until vegetables are completely covered. Cover vegetables with a large plate to prevent 'hats' from coming loose. Set the pot over high heat to bring liquid to a boil. Then, lower heat to medium and cook for 1 1/2 to 2 hours. Cool completely before removing the plate, or use oven mitts and a fork to lift up the plate and to remove it while hot. Serve and enjoy. Yields 6 servings.