Heat the olive oil in a large skillet over medium-high heat. When the oil shimmers, add the sausage. Gently turn it with a spatula for about 5 minutes or until browned. Remove with a slotted spoon, drain, and place in a bowl. Set aside.

Return the skillet to the burner. Add a little more olive oil (if needed) and the onion and cook until the slices start to brown, about 7 minutes. Add the cabbage and cook until it becomes as soft as noodles. Return the sausage to the skillet, mix together, and heat for a minute or two.