Bring a large pot of salted water to boil. Add orecchiette and cook until al dente.
In a medium frying pan add a tablespoon of olive oil and kale stems, cooking over medium heat for 2 minutes. Cover with a lid and reduce heat to low, slowly cooking the stems so they soften for approximately 8 minutes. The kale stems are finished cooking once they are tender but still offer a crunch when bitten into.
In a large skillet, crumble sausage into the pan and cook, breaking apart with a wooden spoon or spatula, until lightly browned. Reduce the heat and add the garlic, cook for another minute.
Add the remaining olive oil, chicken broth, kale, and butter. Stir frequently for 4-5 minutes, scraping the bottom of the pan until the sauce reduces slightly.