Heat the olive oil in a large stock pot or Dutch oven over medium-high heat. Pat the chicken dry and season both sides with salt and pepper. Sear on both sides for 4-5 minutes. It does not have to be cooked all the way through. Remove to a clean plate or cutting board.
2 tablespoons olive oil, 1 1/2 lbs boneless skinless chicken thighs, Kosher salt and pepper to taste
Turn the heat down to medium and add butter and stir to melt. Stir in the onion, carrots, celery, garlic, mushrooms, thyme, and sage. Saute for 3-4 minutes, until the vegetables are soft and fragrant.
1 medium yellow onion, 4 cloves garlic, 2 carrots, 2 celery ribs, 8 oz cremini or button mushrooms, 2 teaspoons thyme leaves, 1 teaspoon fresh sage, 4 tablespoons unsalted butter
Sprinkle the flour over the vegetables and stir to coat to the vegetables. Pour in the broth and stir in the wild rice until combined. Add the seared chicken and push down to submerge it in the broth.
1/4 cup all purpose flour, 4-6 cups chicken bone broth or sugar free chicken broth, 1 cup wild rice
Bring the soup to a rolling boil over medium-high heat then turn the heat down to low and simmer, with the lid on, for 40-45 minutes, until the rice is tender. Stop to stir the rice every 10 minutes so it doesn't stick to the bottom of the pot.
Remove the chicken to a cutting board and shred with two forks or dice into small cubes then stir it back into the soup.
Pour the heavy cream and milk into to the soup and stir to combine. Add more broth or milk to reach your desired consistency. Taste and add more salt and fresh cracked pepper to taste.
1 cup cups whole milk, 1 cup heavy cream
Serve warm with fresh thyme, sage leaves, or grated parmesan cheese.