In a large pot, melt butter and olive oil over medium heat. Add onion, carrots, and celery. Sauté until tender, about 5–6 minutes.
Stir in garlic and cook for 1 minute. Sprinkle flour over the vegetables and stir to coat.
Gradually whisk in chicken broth and bring to a simmer, stirring constantly to avoid lumps.
Pour in the half and half and add the cooked chicken, gnocchi, thyme, salt, and pepper.
Simmer until the gnocchi is cooked through, about 5–7 minutes.
Stir in fresh spinach and let wilt. Taste and adjust seasoning as needed.
Serve warm and enjoy!