Heat a large pot over medium heat and brown the ground beef or sausage.
Add the chopped onion and minced garlic, cooking until softened.
Stir in the diced tomatoes (with juice) and chicken broth.
Bring to a boil, then reduce heat and simmer for 10 minutes.
Add the uncooked penne pasta and cook until al dente (usually 8–10 minutes). If needed, add a splash of broth or water to thin out the soup once the pasta is cooked.
Stir in the dried oregano, salt, and pepper.
Ladle the soup into bowls and top with shredded mozzarella cheese.
Serve hot and enjoy!