Bring a medium saucepan filled with water to a boil. Cook the gnocchi according to package directions. Drain and set aside.
Meanwhile, in a large dutch oven over medium heat, melt the butter. Add the onion, celery and garlic and sauté until the onion becomes translucent, about 7 minutes. Whisk in the flour, forming a roux. Cook for 1 minute. Pour in the cream and milk, and add the carrots and chicken and bay-leafs to the dutch oven. Simmer until the mixture begins to thicken, stirring often, about 5 minutes. Add the chicken broth, and allow the mixture to thicken again, stirring often, about 5 minutes or until the consistency desired is achieved. Stir in the gnocchi, spinach, cheese and seasonings and simmer until soup is heated through.