In a mixing bowl, combine ground beef, bread crumbs, Parmesan, egg, minced garlic, parsley, salt, and pepper until well incorporated.
Roll the mixture into small, bite-sized meatballs.
Heat olive oil in a large pot over medium heat and brown the meatballs in batches; remove and set aside.
In the same pot, add onions, carrots, celery, and mushrooms, sautéing until softened.
Stir in the crushed tomatoes, beef broth, and oregano, bringing the mixture to a gentle simmer.
Return the meatballs to the pot, cover, and simmer for 20 minutes.
While the soup simmers, cook the pasta in a separate pot according to package instructions until al dente; drain and set aside.
Add the cooked pasta to the soup pot just before serving, or distribute into bowls and ladle the soup over the top.
Garnish with fresh basil and additional Parmesan if desired.