Cook the orecchiette according to the package directions. Before draining the orecchiette in a colander, reserve about 1/3 cup of the starchy pasta water.
While the orecchiette is cooking, begin preparing the rest of the recipe. Slice the chicken sausage into medallions.
Add the olive oil and chicken sausage to a large pot and sauté over medium until the chicken sausage begins to brown (about 5 minutes).
Add the minced garlic and butter to the pot with the sausage and continue to sauté for one more minute.
Next, add the chopped kale and reserved pasta water. Turn the heat down to medium-low and continue to cook and stir until the kale has wilted (about 2-3 minutes). Use your spoon to dissolve any browned bits off the bottom of the pot as you stir.
Remove the pot from the heat and stir in the cooked and drained orecchiette. If the pasta and kale are still steaming heavily, let the contents of the pot cool for about 5 minutes, stirring occasionally to release steam. You want the Parmesan to coat the pasta, but not melt.
Once the pasta and kale is hot, but not steaming, add the grated Parmesan, crushed red pepper, salt, and about 15-20 cranks of a pepper mill. Stir to combine, then taste and add more salt if needed. Serve warm.