In a large bowl, combine ground chicken, grated Parmesan cheese, chopped parsley, beaten egg, breadcrumbs, salt, and pepper. Mix until evenly incorporated. Shape the mixture into small meatballs, about 1 inch in diameter.

In a large pot or Dutch oven, heat a splash of olive oil over medium heat. Add the meatballs in batches, ensuring not to overcrowd. Brown them for about 5 minutes, turning to brown all sides. Remove and set aside.

In the same pot, add diced carrots, celery, and minced garlic. Sauté for 3-4 minutes until the veggies begin to soften.

Pour in the chicken broth and bring to a gentle boil. Once boiling, reduce heat to medium-low and add the browned meatballs and chopped spinach. Allow the soup to simmer for 20 minutes.

Before serving, taste and adjust the seasoning with salt and pepper. Ladle the soup into bowls and top with extra grated Parmesan cheese and fresh herbs if desired.