In a skillet, heat some oil over medium-high heat. Brown the chicken pieces on all sides until cooked through. Transfer the chicken to the slow cooker.
In the same skillet, add the mushrooms, onion, and garlic. Cook until the mushrooms are lightly browned and the onions are softened. Transfer the mushroom mixture to the slow cooker with the chicken.
In a mixing bowl, whisk together the chicken broth, heavy cream (or sour cream), flour, dried thyme, dried rosemary, salt, and pepper. Pour the mixture over the chicken and mushrooms in the slow cooker. Stir to combine.
Cover the slow cooker and cook on low for 4-6 hours or on high for 3-4 hours.
Just before serving, sprinkle the shredded cheddar cheese over the casserole. Cover and allow the cheese to melt for a few minutes.
Serve the Slow Cooker Chicken and Mushroom Casserole with Cheese hot, garnished with fresh chopped parsley.
