Set the oven to 350°F (177°C) and prepare a 9x13-inch baking dish by lightly greasing it or lining it with parchment paper.

Generously season the chicken breasts on both sides with kosher salt and freshly ground black pepper. Dredge each piece in all-purpose flour, ensuring an even, light coating. Shake off any excess flour.

Heat the olive oil in a large skillet over medium heat. Once hot, add the chicken and sear each piece until golden brown on both sides, about 3 minutes per side. Note that the chicken does not need to be fully cooked at this stage. Transfer the chicken to the prepared baking dish.

In the same skillet, add the butter and increase the heat to medium-high. Once melted, add the sliced mushrooms, seasoning lightly with salt and pepper. Cook the mushrooms, stirring occasionally, until they are golden brown and tender, approximately 5-6 minutes.

Pour the sherry wine into the skillet, scraping up any browned bits from the bottom of the pan. Allow the mixture to simmer for 1-2 minutes, reducing slightly.

Stir the cream of mushroom soup into the mushroom and sherry mixture, ensuring it is thoroughly combined. Heat the sauce until it is smooth and warmed through.

Arrange the seared chicken in the baking dish and pour the prepared mushroom sauce evenly over the chicken pieces. Top each chicken piece with a slice of Swiss or Muenster cheese.

Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes. Remove the foil and switch the oven to broil. Broil for 1-2 minutes, or until the cheese is bubbly and lightly browned.

Remove the casserole from the oven and let it rest for 5 minutes. Garnish with freshly chopped parsley before serving to enhance both flavor and presentation.