Melt the butter in a large pot over medium heat. Add the onion, carrots, and celery, cooking until softened, about 5 minutes.
Stir in the garlic and cook until fragrant, about 1 minute.
Add the chicken, chicken broth, heavy cream, thyme, salt, and pepper. Bring to a simmer over medium heat.
Stir in the gnocchi and cook until they float to the top, about 3-5 minutes.
Add the spinach and cook until wilted, about 2 minutes.
Taste and adjust seasonings as needed. Serve warm.