Sauté the vegetables. Melt the butter in a large pot over medium heat. Add the onion, celery, and carrots and cook for 5 to 6 minutes until soft.
Add the garlic. Stir in the garlic and cook for 30 seconds until fragrant.
Make the roux. Sprinkle in the flour and stir constantly for 1 to 2 minutes.
Build the broth. Slowly whisk in the chicken broth, bring to a gentle boil, then simmer for 5 minutes until slightly thickened.
Add the cream and seasonings. Stir in the half-and-half, thyme, parsley, salt, and pepper. Keep at a low simmer.
Cook the gnocchi and chicken. Add both and simmer for 3 to 4 minutes, until the gnocchi float and turn plump.
Wilt the spinach. Stir in the spinach and cook for 1 minute.
Taste and serve. Adjust the seasoning and top with Parmesan.