Cook the pasta in well-salted water according to package directions, until al dente. Reserve 1-1½ cups of the pasta water before draining.
Meanwhile, cook and crumble the sausage. Drain on a paper towel-lined plate, leaving 1-2 teaspoons of fat in the pan. Add the chopped kale to the pan along with ¼ cup of pasta water. Saute until wilted, approx. 4-5 minutes.
Add the sausage back to the pan along with the pasta. Add the parmesan cheese and the reserved pasta water, starting with ½ cup, stirring to create the sauce. Add additional pasta water as necessary.
Season to taste with salt and pepper (if needed). Add crushed red pepper flakes for extra heat if desired.