In 4-quart Dutch oven or 12-inch skillet, heat oil over medium heat. Add onion; cook about 4 minutes, stirring frequently, until lightly browned.
Stir in cabbage, broth, tomatoes and pepper. Heat to boiling. Reduce heat to low; cover and cook 20 minutes.
Add sausage; spoon cabbage mixture over sausage. Cover; cook over low heat 10 to 15 minutes longer or until sausage is thoroughly heated and cabbage is tender. Cut sausage into pieces to serve.