Preheat oven to 350°F (175°C) and grease a 9x13 inch baking dish.
Season chicken breasts with salt and pepper on both sides. Dredge in flour, shaking off the excess.
In a large skillet over medium heat, heat the oil. Once hot, brown the chicken on both sides until golden brown, about 3-4 minutes per side. Transfer chicken to the prepared baking dish.
In the same skillet, add butter and increase heat to medium-high. Add mushrooms and season with salt and pepper. Let cook until golden brown and tender, about 5-7 minutes. Stir in sherry and cook for 1-2 minutes more. Stir in cream of mushroom soup, mixing well, and cook until heated through.
Pour the sauce over the chicken in the baking dish. Top with cheese slices.
Cover the dish with foil and bake for 30 minutes. Remove foil and turn oven to broil. Broil until cheese is golden brown, about 1-2 minutes.
Let sit for 5 minutes before serving. Garnish with fresh parsley and enjoy!