Heat a large sauce pot to medium-high heat. Add the oil. Once the oil is heated, add the onions, carrots and celery. Cook for about 5 minutes until vegetables are tender. Add the chicken stock, 2 cups water, wild rice, thyme, rosemary, bay leaf and pepper to the pot. Bring to a low boil and cook for about 45 minutes. Stir in chicken, milk and half-and-half and cook for 5 minutes. In a small bowl, combine the cornstarch and 1/4 cup water. When the soup begins to boil, slowly whisk in the cornstarch slurry and cook for a few minutes to thicken. Remove soup from heat, and remove the bay leaf before serving.