In a large pot or Dutch oven over medium-high heat, cook the sausage, breaking it up with a wooden spoon, until browned, about 5-7 minutes.
Add the diced onion and cook until softened, about 3-4 minutes. Stir in the garlic and red pepper flakes, cooking for another minute until fragrant.
Pour in the crushed tomatoes and chicken broth, scraping up any browned bits from the bottom of the pot. Bring to a boil.
Add the pasta and stir well. Reduce heat to medium and cook, stirring occasionally, for about 10-12 minutes until the pasta is almost tender.
Stir in the chopped kale and cook for another 3-4 minutes until the kale is wilted and the pasta is fully cooked.
Remove from heat and stir in the Parmesan cheese. Season with salt and pepper to taste. Let stand for 2-3 minutes to thicken slightly before serving.