Saute the Vegetables: Heat the butter and olive oil in a large Dutch oven or soup pot over medium heat. Add the diced onion, celery, and carrot. Cook for 5 to 6 minutes, stirring occasionally, until the vegetables have softened and the onion is translucent.

Add the Garlic: Stir in the minced garlic and cook for 1 additional minute until fragrant.

Create the Roux: Sprinkle the all-purpose flour evenly over the softened vegetables. Whisk continuously for 1 to 2 minutes to cook out the raw flour taste. The mixture will look like a thick paste.

Whisk in the Liquids: Slowly pour in the chicken broth and the half-and-half, whisking constantly to ensure no lumps form from the flour mixture. Add the dried thyme, salt, and black pepper.

Simmer: Bring the soup to a gentle simmer over medium heat. Do not let it come to a rapid boil, as the dairy can curdle. Let it simmer uncovered for about 5 minutes to allow the broth to thicken slightly.

Cook the Gnocchi: Add the package of potato gnocchi to the simmering soup. Cook for 3 to 4 minutes, or until the gnocchi float to the top of the broth, which indicates they are fully cooked.

Add Chicken and Spinach: Stir in the shredded cooked chicken and the chopped fresh baby spinach. Let the soup simmer for 1 to 2 more minutes just until the chicken is heated through and the spinach has completely wilted.

Serve: Taste the soup and adjust the salt and pepper if necessary. Ladle the hot soup into bowls and serve immediately with crusty bread or breadsticks for dipping.