In a large pot, cook carrot, celery and leek (or onion) in the melted butter over medium heat until the vegetables are tender. Cooking the vegetables first, before adding stock, adds a lot of flavor.
Season with salt and pepper. Add the wild rice, chicken stock, rosemary, thyme, celery seed, and bay leaves.
Raise the heat slightly to allow soup to simmer, covered, for 20 minutes.
Add chicken pieces, and simmer for approximately 20 minutes more until chicken is cooked and rice is tender.
To finish the soup, add the zest of one lemon and lemon juice, whole milk, and cream. Season with more salt and pepper to taste.
To thicken the soup, melt 1⁄4 cup of butter in a separate small pot and whisk 1⁄4 cup of flour into it and stir for a minute or two.
Add this flour and butter paste to the soup to thicken. Repeat if you like your soup extra thick.
Bring the soup back up to temperature and serve with fresh thyme sprinkled on top.
Unfortunately, this soup doesn’t freeze well because it contains cream and rice. The cream may curdle and the rice can get mushy.