Preheat the oven to 375 degrees F (190 degrees C).
Slice peppers 1/2-inch from the top; cut out stems and set aside tops. Cut core from the inside of peppers and strip away any seeds. Cut off a thin slice from the bottoms so peppers can stand upright. Poke about 4 tiny holes in the bottoms to let juices drain.
Pour 2 1/2 cups tomato sauce into a 9x13-inch baking dish. Add onion, beef broth, and red pepper flakes; spread out mixture evenly over the bottom. Set bell peppers upright in the dish.
Combine ground beef, cooked rice, Parmigiano-Reggiano cheese, 2 tablespoons tomato sauce, 1/4 cup parsley, garlic, salt, and black pepper in a large mixing bowl.
Lightly stuff peppers with meat mixture. Spread 1 tablespoon tomato sauce on top of each portion of stuffing; place reserved tops onto peppers. Lay a piece of parchment paper loosely on top of peppers and cover the dish tightly with foil. Place the dish on top of a baking sheet.
Bake in the preheated oven until peppers have softened slightly, about 1 hour. Remove foil and parchment paper. Continue baking until meat filling is cooked through and peppers are tender, 20 to 30 more minutes.
Sprinkle each pepper with 1/2 teaspoon parsley and drizzle with a spoonful of pan juices.