In a large skillet, sauté the sausages over medium-high, breaking up meat with a wooden spoon, until browned, about 5 minutes. Add chopped leeks to sausage in skillet and cook until softened, about 5 more minutes. Add kale and cook until wilted. Add wine and cook, stirring frequently and scraping up any brown bits on the bottom of the pan, until mostly evaporated. Stir in butter and season to taste with salt and pepper.

Meanwhile, in a large pot of boiling water, cook pasta according to package instructions. Reserve 1/2 cup pasta water. Drain pasta, return to pot, add sausage mixture, and toss to combine, adding reserved pasta water as needed to thicken sauce. Toss in the shredded Parmesan and Asiago. Adjust salt and pepper as needed and serve.