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 heated through, about 10 minutes while adding in spinach during the last minute of cooking. Serve warm, sprinkle each serving with parmesan cheese.
**If you like a brothier soup you can reduce pasta to 3/4 cup. Note that as the soup sits the pasta will absorb more broth so you can add more broth to thin the soup as desired.