Cook pasta according to package directions. Drain, reserving 1/2 cup pasta cooking water.
Heat oil in a dutch oven. add sausage and sauté , crumbling about 5 minutes. Add garlic, crushed red pepper and half the broth. stirring to loosen brown bits on the bottom of pan. add kale and cook until wilted. Add remaing broth, cover and cook until kale is tender, about 5 minutes.
Add cooked pasta and reserved pasta water to sausage mixture, cook 2 minutes. Toss with cheese and serve.