Heat the butter and olive oil in a large Dutch oven over medium heat. Add the diced onion, minced garlic, sliced mushrooms, and diced carrots.
Cook for 6 to 8 minutes, stirring occasionally, until the mushrooms brown lightly and the carrots begin to soften. Add the dried thyme and dried parsley, and cook for 1 minute.
Pour in the uncooked long-grain rice and stir to combine with the vegetables. Add the chicken broth and mix everything together.
Bring the mixture to a boil. Reduce the heat to low, cover the pot, and simmer for 15 to 18 minutes, or until the rice is tender and fully cooked.
Stir in the shredded turkey and pour in the heavy cream. Let the soup warm through for 3 to 5 minutes, stirring occasionally, until the texture becomes creamy.
Season with salt and black pepper to taste. If the soup thickens, add a splash of broth to loosen the consistency. Ladle the soup into bowls and garnish with fresh thyme and black pepper before serving.