In a medium bowl, combine ground beef, bread crumbs, Parmesan, half the garlic, parsley, half the salt, and half the pepper. Mix gently and form into small meatballs.
Heat 1 tablespoon olive oil in a large pot over medium-high heat. Brown the meatballs on all sides, then remove and set aside.
In the same pot, add butter and remaining tablespoon of olive oil. Sauté onion, celery, and carrots until softened, about 5 minutes.
Add mushrooms and remaining garlic, cooking until fragrant.
Pour in the beef broth and crushed tomatoes. Add dried basil and remaining salt and pepper. Bring to a simmer.
Return meatballs to the pot and simmer for 15-20 minutes until cooked through and vegetables are tender.
Serve hot, garnished with extra Parmesan or fresh parsley if desired.