Add beef and pork to a large mixing bowl. Add in the bread crumbs, parsley, Parmesan, egg, 1 teaspoon of salt, and 1/4 teaspoon of black pepper.
Gently toss and break up the mixture with hands to coat and distribute. Shape mixture into very small meatballs, about 3/4 inch to 1-inch round and transfer to a large plate.
Heat 1 tablespoon olive oil in a large Dutch oven over medium-high heat. Add meatballs and cook until browned, turning occasionally to brown on all sides, about 5 or 6 minutes total. Transfer the meatballs to a plate lined with paper towels.
For the soup:
Heat 1 tablespoon olive oil in a large pot over medium-high heat. Add carrots, onions, and celery and sauté until veggies have softened about 6 to 8 minutes. Season with salt, pepper, and Italian seasoning, then add garlic and sauté 1 minute longer.
Stir in orzo, then add chicken broth; season with salt and pepper to taste and bring to a boil. Add meatballs, reduce heat to a light boil (about medium or medium-low heat.) Cover and cook, stirring occasionally until pasta is tender and meatballs are cooked through, about 10 minutes while adding spinach during the last minute of cooking.
Serve warm and sprinkle with Parmesan cheese.
Store leftover soup in a sealed container in the refrigerator for up to 3 days.