In a large bowl, combine ground beef, Parmesan cheese, egg, Italian seasoning, salt, pepper, and panko breadcrumbs. Mix well.
Roll the mixture into 1-inch meatballs.
Heat olive oil in a large pot or Dutch oven over medium heat. Brown the meatballs on all sides; remove from pot and set aside.
Add carrots, celery, and onion to the pot and cook until softened, about 5-7 minutes.
Pour in chicken broth and add bay leaves. Bring to a boil, then reduce heat and simmer for 15 minutes.
Gently add the meatballs to the pot and simmer for another 15 minutes, or until cooked through.
Stir in fresh parsley before serving.