Fill a large stockpot with water and bring to a boil over a high heat. Add 1 tablespoon salt and the bell peppers. Cook until the peppers just begin to soften, 3 to 5 minutes, using a spoon to keep the peppers submerged in the water. Using tongs or a slotted spoon, remove peppers from the pot, drain off excess water, and set aside to cool.
In a large skillet over medium-high heat, saute the sausage, onion and garlic together until the sausage is browned and no longer pink. Remove from the heat and stir in the rice, tomato sauce, cheese and basil. Season with salt and pepper.
Place the peppers cut-side up in a baking dish large enough to hold them all (it will vary depending on the size of your peppers). Using a large spoon, divide the filling evenly amount the peppers. Drizzle a little of the beef broth evenly over top of the peppers, and then pour the rest into the bottom of the pan. Bake until heated through, 25 to 30 minutes. Serve immediately.