Brown sausage in a large pot or Dutch oven over medium-high 5-7 minutes, breaking up with a wooden spoon.
Cook onion 3-4 minutes until softened; add garlic and pepper flakes and cook another minute until fragrant.
Add tomatoes and broth, scraping up browned bits; bring to a boil.
Stir in pasta; reduce heat to medium and cook 10-12 minutes, stirring occasionally, until almost tender.
Add kale; cook another 3-4 minutes until wilted and pasta fully cooked.
Off heat, stir in Parmesan; season with salt and pepper and stand 2-3 minutes to thicken slightly.