In a bowl, combine the beef, pork, egg, breadcrumbs, Parmesan, parsley, garlic, salt, and pepper. Mix gently just until combined. Roll into small 3/4-inch meatballs and set aside.
Heat the olive oil in a large Dutch oven over medium heat. Add the onion, carrots, and celery; cook 5 to 6 minutes, stirring, until beginning to soften.
Pour in the chicken broth and bring to a gentle boil. Add the pasta and cook according to its package timing, stirring occasionally.
Lower the heat to a steady simmer and carefully add the meatballs. Cook 6 to 8 minutes, until the pasta is tender and meatballs reach 160°F (71°C) at the center.
Stir in the spinach and cook 1 to 2 minutes, just until wilted. Taste the broth and adjust salt and pepper.
Ladle into bowls and serve with extra Parmesan and parsley.