Heat 2 tablespoons of the oil in a large skillet. Add the sausage, breaking it up with a wooden spoon, and cook over moderately high heat until no pink remains, 5 minutes. Add the onion and garlic. Cook, stirring occasionally, until the onion is softened and the sausage is browned, 5 minutes. Stir in the bread crumbs. Let cool. Stir in the cheese and parsley; season with salt and pepper.