Position rack in upper third of oven; preheat broiler.
Place peppers cut-side down in a large microwave-safe dish. Fill the dish with 1/2 inch of water, cover and microwave on High until the peppers are just softened, 7 to 10 minutes. Drain the water and transfer the peppers to a roasting pan.
Meanwhile, cook sausage in a large nonstick skillet over medium-high heat, breaking it up into small pieces with a wooden spoon, until cooked through, about 5 minutes. Stir in broth, tomatoes and rice; increase heat to high and bring to a simmer. Cover, reduce heat to medium-low and simmer until the rice is softened but still moist, 5 minutes. Remove from the heat and let stand, covered, until the rice absorbs the remaining liquid, about 5 minutes.
Stir basil and half the cheese into the rice mixture. Divide the filling among the peppers, then top with the remaining cheese. Broil until the cheese is melted, 2 to 3 minutes.
6 servings