Preheat your oven to 375F and position the rack in the top third of the oven.

Cut the chicken breasts in half lengthwise to make 6 thinner cutlets. Season both sides with salt & pepper and coat in flour, shaking off any excess.

Add the oil and 1 tablespoon of the butter to a skillet over medium-high heat. Cook chicken in two batches for 3-4 minutes per side until lightly browned. Transfer chicken to the casserole dish.

Add 1 tablespoon of butter to the skillet. Once melted, add the mushrooms and cook until seared, about 5 minutes. Transfer mushrooms to the casserole dish.

In the same skillet, melt the remaining 2 tablespoons of butter over medium heat. Add flour and garlic, cooking for about a minute while stirring.

Pour in the sherry, then slowly whisk in the cream until smooth. Cook for a few minutes until slightly thickened.

Pour the cream sauce over the chicken and mushrooms.

Top with cheese slices.

Cover the casserole with foil and bake for 20 minutes.

Remove the foil and broil until the cheese is browned, watching carefully.

Let the chicken rest for a few minutes, then serve.