Panera Cream of Chicken and Wild Rice Soup

1 cup long grain rice
1/2 cup wild rice
1 cup celery, diced
1 medium onion, diced
1 cup carrots, diced
1 tablespoon olive oil
1 cup cooked chicken
1 teaspoon thyme
2 cans chicken broth
2 tablespoons cornstarch
4 tablespoons water
2 cups whole milk

Cook the rice separately and according to the package instructions.
In a large pot, saute the diced celery, onion, and carrots in olive oil until the onion is translucent. Add the thyme and season to taste with salt and pepper. Stir for 1 minute, then add the chicken broth and simmer for 20 minutes.
Add the milk and bring back to a simmer.
Stir together the cornstarch and water. Add the mixture to the soup. Let simmer until slightly thickened, stirring.
Add the rice and chicken to heat through. Serve immediately or refrigerate.