In a 4- or 5-quart pot, heat the olive oil over medium heat until hot and rippling. Add the chopped onion, carrots and thyme. Cook until the onion is translucent and carrots are slightly tender, stirring often, about 4-5 minutes. Stir in the garlic and cook, stirring constantly, until fragrant.
Whisk in the flour and cook, whisking or stirring constantly, until the flour is lightly golden, 1-2 minutes. Slowly whisk in the half-and-half. Whisk in the milk and chicken broth. Stir while bringing the mixture to a boil over medium to medium-high heat.
Cook, stirring often, until the mixture is slightly thickened, 5-7 minutes. Stir in the uncooked gnocchi and simmer over medium-low heat for 3-4 minutes, stirring occasionally. The soup should thicken up quite a bit while the gnocchi is cooking. Stir in the chicken and spinach and cook for 1-2 minutes until heated through. Season with salt and pepper to taste and serve.
Thickness: this soup is thick and hearty. If you like a less thick soup, simply add more liquid (either milk or chicken broth). I'd suggest adding it at the end with the chicken and spinach, after the soup has thickened. Gnocchi: vacuum-sealed packages of gnocchi are usually in the pasta aisle of the grocery store. I've also seen frozen gnocchi, too, so check both places if you can't find it.