In a large pot, heat the butter and olive oil over medium-high heat. Add the diced onion, chopped celery, and minced garlic. Sauté until the onion becomes soft and translucent.
Next, sprinkle the flour over the sautéed vegetables and stir until well combined. Cook this mixture for 1 minute to eliminate any raw flour taste.
Gradually pour in the fat-free evaporated milk or half and half while stirring constantly. This will help prevent any lumps from forming.
Meanwhile, take another pan and cook the gnocchi according to the package directions. Once they float to the surface, drain them and set aside.
Now, go back to the soup pot and add the diced chicken and shredded carrots. Stir well as the mixture starts to thicken slightly.
Pour in the chicken stock along with the cooked gnocchi, chopped spinach, dried thyme, salt, and pepper. Cover the pot and let it simmer for about 5 minutes, allowing the flavors to meld together and the spinach to wilt.
Finally, taste your creation and adjust the seasoning if needed. Serve this delicious soup hot, garnished with fresh parsley or grated Parmesan cheese if you desire.