Preheat oven to 375°F 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 of each piece with salt & pepper, then coat each piece in flour. Shake off any excess flour.

Add the oil and 1 tablespoon of butter to a skillet over medium-high heat. Let the pan heat up for a few minutes. Cook the chicken in two batches, lightly browning each piece of chicken for about 3-4 minutes per side. Transfer the chicken to a 9×13 casserole dish as you finish browning each batch. Add a splash more olive oil to the second batch if the pan is dry.

Add 1 tablespoon of butter to the same skillet you cooked the chicken in. Once it melts, add the mushrooms and cook them until they’re seared and their water is released and cooked off (about 5 minutes). Transfer the mushrooms to the casserole dish.

In the same skillet, over medium heat, add the remaining 2 tablespoons of butter. Once it melts, add the flour and garlic. Cook for about a minute, stirring constantly.

Pour in the sherry and then slowly whisk in the cream until the flour has dissolved and you’ve got a smooth sauce. Cook it for a few minutes until it thickens up a bit. Add a bit of salt & pepper to the sauce.

Pour the cream sauce over the chicken and mushrooms.

Top the chicken with the cheese slices.

Cover the casserole with foil and bake for 20 minutes.

Remove the foil and broil for a few minutes until the cheese has browned.

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