Preheat the oven to 375°F (190°C). Lightly grease or line a baking sheet with parchment paper.
In a large bowl, combine the ground beef, garlic, Italian seasoning, beaten egg, Parmesan cheese, flour, salt, and black pepper.
Mix gently until just combined, taking care not to overwork the mixture.
Shape the mixture into small meatballs about ½ to ¾ inch in diameter and place them on the prepared baking sheet.
Bake for 8 to 10 minutes, or until lightly browned. The meatballs do not need to be fully cooked at this stage.
While the meatballs bake, heat the olive oil in a large soup pot over medium heat.
Add the onion and carrots, then cook for 8 to 10 minutes, stirring occasionally, until the vegetables begin to soften.
Stir in the crushed tomatoes, tomato sauce, beef broth, and Italian seasoning.
Season with salt and black pepper, then bring the soup to a gentle simmer.
Carefully add the baked meatballs and pasta to the pot.
Simmer uncovered for 10 to 12 minutes, or until the pasta is tender and the meatballs are fully cooked.
Stir in the chopped parsley.
Ladle the soup into bowls and garnish with grated Parmesan cheese if desired.