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 the hot butter and oil until vegetables are soft, 8 to 10 minutes. Stir flour into mixture, coating vegetables; cook 2 more minutes.
Stir chicken broth into vegetables, stirring 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 slightly thickened, about 5 more minutes. Gently fold chicken, gnocchi, and spinach into soup. Season with salt, black pepper, thyme, and nutmeg. Adjust thickness by adding more chicken broth, if desired.
