Heat a medium sauce pot, at least 10 cups, over medium-high heat. Add the oil, then add the carrots, onions, and celery to the warm pot, and stir until tender.
Add the chicken stock and cook until reduced down to about 4 cups. Then add the turkey, rice, rosemary, thyme, salt, and pepper. Then add the milk, and let the soup come back up to temperature.
Combine the arrowroot with the water and whisk until fully incorporated.
Add the arrowroot mixture to the soup, bring back to a low boil, and whisk in the slurry until the soup thickens to a chowder consistency. Serve hot.