Use a 6-quart slow cooker. In a large skillet over medium heat, add the beef, onion, mushrooms, and garlic. Cook until the meat is no longer pink. Drain any accumulated fat. Transfer the meat mixture to your slow cooker.
Add the broth, tomatoes, celery, and carrots. Stir in the oregano and salt. Cover and cook on low for 7-8 hours or on high for about 4 hours. Stir in the pasta, cover, and cook on high for an additional 20 minutes or until the pasta is bite-tender.
Garnish with freshly grated Parmesan cheese, if desired.