In a 5- to 6-quart pan over medium-high heat, combine butter and oil. Add sausages and break apart with a spoon; stir often until lightly browned, about 5 minutes. Add cabbage, broth, and parsley, and bring to a boil. Reduce heat, cover, and simmer, stirring occasionally, until cabbage is tender to bite, about 30 minutes.
Spoon sausage and cabbage mixture into bowls. Add salt and pepper to taste.