In a large soup pot over medium heat, melt the butter. Add the onion and celery and cook, stirring occasionally, until the onion is translucent and lightly browned around the edges, about 5-7 minutes. Add the garlic and cook until fragrant, about 30-60 seconds.
Sprinkle in the flour and stir constantly as the flour cooks, about 1-2 minutes.
Slowly whisk in the half and half and simmer until thickened, about 4-6 minutes.
Whisk in the chicken broth and simmer until thickened again about 2-4 minutes.
Add the Carrots, spinach leaves, parsley, thyme, chicken, and gnocchi. Continue to cook until all the ingredients are just heated through.
Season to taste with salt and pepper. Serve with grated Parmesan cheese.