Coat the bottom of a skillet liberally with olive oil. Cook and stir sausage over medium heat until brown, 5 to 7 minutes. Transfer to a plate.
Drizzle a little more olive oil into the skillet. Cook onions over medium-high heat until just beginning to brown, about 15 minutes. Add sausage and kale to the skillet, and cook until kale begins to wilt, about 2 minutes. Season with salt and pepper.