Cook rigatoni in salted water according to package directions; drain.

Meanwhile, remove sausage from casing and cook in a large nonstick skillet over medium heat, breaking up as it cooks, about 3 minutes. Add kale; cook, stirring frequently, until limp, 3-5 minutes.

Add broth to skillet and scrape up browned bits with a wooden spoon; season with salt and pepper. Cover, reduce heat to low; cook until kale is tender, 5-10 minutes. Stir in rigatoni; heat through.

Sprinkle each serving with about 2 tbsp of cheese before serving.