Young chefs will get a kick out of loading up the peppers' bowl-shaped interiors and sprinkling them with Parmesan.
Slice the top 1/4 inch off each pepper. Finely chop the flesh on the stem end; set it aside. Remove the seeds and white pith from inside the peppers. (If the peppers won't stand up straight, take a small slice off the bottom with a paring knife to make a flat surface.)
Put a steamer basket (or a colander) inside a large pot and add an inch or so of water. Place the peppers in the basket. Bring the water to a boil and tightly cover the pot. Steam the peppers for 8 minutes. Remove the peppers with tongs and set them on a wire rack to cool.
Combine the reserved chopped pepper, ground beef, onion, and garlic in a large skillet. Brown the meat over medium heat for 5 to 6 minutes, breaking it up with a wooden spoon.
Drain any visible fat from the pan, then return it to the heat. Add the rice, broth, tomato, paprika, Worcestershire sauce, basil, salt, and pepper. Bring the mixture to a boil, then reduce the heat and simmer it, tightly covered, for 18 to 20 minutes, or until the liquid is absorbed. Remove the pan from the heat and let it stand for 15 to 20 minutes. Stir in the egg and the 1/3 cup of Parmesan.
Heat the oven to 375 degrees. Lightly oil a large baking dish or casserole and pour in 2 1/2 cups of tomato sauce. Using a large spoon, scoop about 3/4 cup of filling into each pepper. Set the stuffed peppers into the prepared pan, so they are evenly spaced and surrounded by sauce. Spread a spoonful of the remaining sauce over the top of each, to keep the filling moist, and cover the pan with aluminum foil.
Bake the peppers until they're heated through, about 35 minutes. Remove the foil and sprinkle the tops with Parmesan. Serve the peppers hot, in pools of tomato sauce. Makes 6 servings.