Melt the butter in a large stock pot. Add the onions, carrots, and celery. Cook until the onion is translucent and soft. Add garlic and cook for one minute.
Add flour and mix well. Slowly stir in the half and half, wild rice, stock, salt, pepper, thyme, and rosemary.
Bring to a boil then reduce the heat to medium-low, and cover. Cook until rice is cooked; 45 minutes to an hour.
Add the turkey to the pot and cook for another 5 minutes until heated though.
Remove the bay leaf. Ladle the soup into bowls and garnish with parsley.