In a large mixing bowl, combine ground beef, ground pork, breadcrumbs, grated Parmesan cheese, chopped parsley, egg, minced garlic, salt, and pepper. Mix until well combined. Shape the mixture into small meatballs, about 1 inch in diameter.
Heat olive oil in a large pot over medium heat. Add meatballs and cook until browned on all sides. Remove meatballs from the pot and set aside.
In the same pot, add chopped onion, carrots, and celery. Sauté until the vegetables are softened.
Pour in the chicken broth and bring the mixture to a simmer. Add the acini di pepe pasta and let it cook according to the package instructions or until al dente.
Return the cooked meatballs to the pot. Add chopped spinach and let the soup simmer until the meatballs are cooked through and the spinach is wilted.
Season the soup with salt and pepper to taste. Adjust the seasoning if necessary.
Ladle the soup into bowls and sprinkle each serving with grated Parmesan cheese.