Melt the butter and olive oil together in a large pot over medium-high heat.
Add the diced onion, celery, and minced garlic and cook until they soften and become fragrant.
Stir in the flour and continue cooking for about one minute to make a roux.
Gradually pour in the half-and-half and chicken broth while stirring constantly until the mixture thickens.
Mix in the fresh thyme, shredded carrots, chopped spinach, cooked chicken, and potato gnocchi.
Lower the heat and let the soup simmer for around 5 minutes until the gnocchi is tender and the soup has thickened.
Season with salt and pepper according to your taste, then serve the soup hot.