Add beef and pork to a large mixing bowl. Add in bread crumbs, parsley, oregano, parmesan, egg, 1 tsp salt and 1/4 tsp pepper.
Gently toss and break up mixture with hands to evenly coat and distribute. Shape mixture into very small meatballs, about 3/4 inch to 1 inch and transfer to a large plate.
Heat 1 Tbsp olive oil in a large non-stick skillet over medium-high heat. Add half of the meatballs and cook until browned, turning occasionally (to brown on 2 or 3 sides), about 4 minutes total.
Transfer meatballs to a plate lined with paper towels while leaving oil in skillet. Repeat process with remaining meatballs (note that meatballs won't be cooked through at this point, they'll continue to cook through in the soup).
For the soup:
While meatballs are browning, heat 1 Tbsp olive oil in a large pot over medium-high heat. Add carrots, onions and celery and saute until veggies have softened about 6 - 8 minutes, add garlic and saute 1 minute longer.
Pour in chicken broth, season soup with salt and pepper to taste and bring mixture to a boil. Add in pasta and meatballs, reduce heat to light boil (about medium or medium-low).
Cover and cook, stirring occasionally until pasta is tender and meatballs have cooked through, about 10 minutes, while adding in spinach during the last minute of cooking. Serve warm, sprinkle each serving with Parmesan cheese.