Melt butter with olive oil in a large soup pot over medium heat. Cook and stir zucchini, celery, onion, red bell pepper, carrots, and garlic in hot butter-oil until vegetables are soft, 8 to 10 minutes. Stir in flour until vegetables are coated; cook for 2 more minutes.

Pour in chicken broth and stir until flour paste combines with broth and soup is thick and smooth, about 5 minutes. Pour in both kinds of half-and-half; bring to a simmer. Cook until soup is slightly thickened, about 5 more minutes.

Gently fold chicken, gnocchi, and spinach into soup. Season with thyme, nutmeg, salt, and pepper. Adjust thickness by adding more chicken broth, if desired.