Place a large pot of salted water on the stove to boil. Once boiling, add the spaghetti and cook until al dente. Drain pasta but reserve 1/3 cup cooking water. Set aside.
Heat the olive oil over medium heat in a heavy skillet and add the sausage, breaking up into small clumps with a wooden spoon. Cook until sausage is done and then add the chopped kale.
Continue cooking the kale and sausage mixture until the kale has wilted. Then, add the cream and stir.
Add cooked spaghetti to your skillet and stir well to combine. Add the cooking water --- only enough so your pasta is not dry. Just add a little at a time here.
Season to taste with salt and pepper and serve immediately.