Cut the chicken breasts into thinner cutlets by slicing lengthwise. Season each piece with salt and pepper, then lightly coat in flour. This helps the chicken brown nicely while keeping it tender inside.
Heat olive oil in a large skillet over medium heat. Pan-fry the chicken for a few minutes on each side until golden. Transfer the cooked pieces to a baking dish and set aside.
In the same skillet, add butter and sauté sliced mushrooms until tender. Stir in garlic during the last minute of cooking to release its aroma. Spread the mushrooms over and around the chicken in the baking dish.
Pour sherry into the skillet and let it reduce slightly. Add heavy cream and simmer until it reaches a creamy, Alfredo-like consistency. Pour this sauce over the chicken and mushrooms evenly.
Layer sliced Muenster cheese on top of the chicken. Cover with foil and bake at 350°F for 20 minutes. Remove the foil, broil briefly to brown the cheese, and serve immediately.