In a large soup pot or Dutch oven, heat the olive oil and butter over medium heat. Add the onion, celery, carrot, and ½ teaspoon of the salt.
Cook for 5-6 minutes, stirring occasionally, until the veggies begin to soften. Stir in the garlic, thyme, and black pepper, cooking for 30 seconds more.
Sprinkle the flour over the vegetables and stir for 1 minute until fully absorbed.
Slowly pour in the chicken broth, stirring constantly to avoid lumps. Add ½ teaspoon of salt along with the chicken pieces. Bring to a gentle boil, then reduce to a strong simmer, cover, and simmer for 5 minutes.
Uncover, add the gnocchi, then cover and simmer for 8-10 minutes, or until the gnocchi are tender and cooked through, stirring once or twice.
Carefully remove the chicken pieces to a cutting board. Dice to shred into small bite-sized pieces. Add back to the pot.
Stir in the cream, Parmesan, and spinach. Simmer for another 1-2 minutes until the spinach is wilted and everything is warmed through.
