Cheesy Sausage without drippings vegetables

1 lb spicy ground pork sausage (like Jimmy Dean hot sausage) 1 tablespoon vegetable oil 1 tablespoon butter 1 yellow onion , chopped 2 carrots , diced 3[...]

1 lb Italian sausage (casings removed, can use more if desired) 1 medium onion , finely chopped 3 tablespoons oil or 3 tablespoons butter 1 (10 ounce) can[...]