In a 4-quart Dutch oven cook sausage, mushrooms, onion, and celery over medium heat until sausage is browned, stirring to break up sausage as it cooks. Drain fat.
Add caraway seeds and pepper to sausage mixture in Dutch oven. Add beef broth and beer; bring to boiling. Add potatoes. Simmer, covered, for 10 minutes. Add broccoli. Simmer, covered, about 5 minutes more or until potatoes and broccoli are tender.
Stir cabbage and milk into sausage-broccoli mixture. Cook for 2 to 3 minutes or just until cabbage is tender and soup is heated through.