Season both sides of the chicken with salt and pepper, dredge lightly in flour to coat both sides. Shake off excess.
Add oil to frying pan and brown chicken in batches on both sides. You don’t need to cook the chicken completely. It will finish cooking in the oven. Transfer the chicken to a 9×13-inch baking dish.
Add the butter to the frying pan and let it melt over medium high heat. Add mushrooms, season with salt and pepper and brown mushrooms until golden. Then add the sherry wine and cook for another minute or two. Add the creamy mushroom soup and milk and mix well.
Pour sauce over the chicken breasts, cover with foil and bake in oven for about 30 minutes. Remove from oven and top each piece of chicken with one slice of Muenster cheese. You can fold the cheese in half if it is too wide for the breast.
Place chicken back in oven uncovered and broil for 1-2 minutes to brown the cheese. Remove from the oven and set aside to cool.