Preheat Oven: Preheat your oven to 350°F (177°C). Lightly grease or line a 9×13-inch baking dish with parchment paper.

Season and Prepare Chicken: Season both sides of the chicken breasts with kosher salt and freshly ground black pepper. Dredge each piece in flour, shaking off any excess.

Brown the Chicken: Heat olive oil in a large skillet over medium heat. Add the chicken and brown on both sides (no need to cook through at this stage). Transfer the chicken to a plate and set aside.

Sauté Mushrooms: In the same skillet, melt the butter over medium-high heat. Add the mushrooms, season with salt and pepper, and sauté until golden brown. Deglaze the skillet by pouring in the sherry wine and cooking for 1-2 minutes.

Prepare the Sauce: Stir the cream of mushroom soup into the skillet with the mushrooms and sherry, mixing well. Heat until the sauce is evenly warmed.

Assemble the Casserole: Arrange the browned chicken pieces in the prepared baking dish. Pour the mushroom and soup sauce over the chicken. Top each piece of chicken with a slice of Swiss or Muenster cheese.

Bake: Cover the dish with aluminum foil and bake for 30 minutes in the preheated oven. After baking, remove the foil and broil for 1-2 minutes, until the cheese is bubbly and lightly browned.

Rest and Garnish: Remove the casserole from the oven and let it rest for 5 minutes. Garnish with freshly chopped parsley before serving.