In a very large skillet heat oil over medium heat. Add sausage and onion wedges; cook and stir 6 to 8 minutes or until browned.
Add oregano and garlic to skillet. Cook for 1 minute. Add broth. Bring to boiling; reduce heat. Boil gently, uncovered, 3 to 4 minutes or until reduced by about half. Gradually add greens, tossing until wilted before adding more. Add butter beans and vinegar; heat through. Sprinkle with cheese.