Heat the olive oil in a large pot over medium heat.
Add the onions and celery and cook, stirring constantly, for 2 minutes.
Add the garlic and cook for 30 seconds.
Sprinkle the flour over the vegetables and whisk for 1 minute.
Whisk in the chicken broth, cream, and milk. Bring to a simmer, whisking constantly, until soup has thickened slightly, about 5 minutes.
Add the chicken, spinach, gnocchi, carrots, thyme, salt, and pepper and stir.
Continue simmering for 10 minutes or until gnocchi and carrots are tender and cooked through.