Heat olive oil in a large pot over medium heat.
Add diced onions, carrots, and celery; sauté until softened, about 5 minutes.
Stir in minced garlic and cook for another minute.
Add the diced chicken and cook until browned on all sides.
Pour in the chicken broth and bring to a boil.
Reduce heat and let simmer for 10 minutes.
Add gnocchi and cook until they float, about 3-5 minutes.
Stir in heavy cream and fresh spinach.
Season with salt and pepper to taste.
Serve hot, garnished with fresh herbs if desired.