Step 1

Set a wire rack inside a rimmed baking sheet. Cut two 12-inch sheets of plastic wrap.

Step 2

Cut the chicken breasts in half lengthwise, making 6 roughly equal pieces; they should look like large chicken tenders. Place one sheet of plastic on a clean cutting board. Put a chicken piece in the center of the plastic and top with the other sheet of plastic. Pound the chicken with the flat side of a meat mallet, starting in the center and working your way to the edges, until the chicken is 1/4 inch thick and 6 to 8 inches long. Transfer to the wire rack. Repeat with the remaining chicken pieces. Liberally sprinkle the chicken with salt and pepper.

Step 3

Mix the flour with 1 1/2 teaspoons salt and a generous amount of pepper in a shallow bowl or plate. Dredge the cutlets in the seasoned flour, shaking off any excess. Heat 3 tablespoons of the oil in a large skillet over medium-high heat until very hot, about 1 minute. Sear 3 cutlets until golden brown, about 2 minutes per side. Transfer the cutlets to a plate. Add the remaining 1 tablespoon of oil to the pan and sear the remaining 3 cutlets until golden brown, about 2 minutes per side. It's ok if the chicken is not completely cooked through; it will finish cooking in the sauce.

Step 4

Add the mushrooms and 1/2 teaspoon salt to the same pan and cook, stirring and scraping up any browned bits, until the mushrooms are slightly softened and just beginning to release some liquid, 3 to 4 minutes. (The mushrooms will soak up the oil quickly and dry up the pan; that's ok, more liquid will release as they cook longer.) Add the shallots and cook, stirring and scraping up any browned bits, until starting to soften, 3 to 4 minutes.

Step 5

Remove the pan from the heat. Pour in the wine and 1/2 cup water. Return the pan to high heat and bring to a boil. Reduce the heat to medium and simmer until the liquid reduces by a third and starts to thicken, 6 to 7 minutes. Whisk in the butter and continue whisking until it is melted and the sauce has thickened, 1 to 2 minutes.

Step 6

Add the cutlets and any accumulated juices to the pan and cook, flipping halfway through, until the chicken is cooked through and the sauce has thickened, about 2 minutes.

Step 7

Remove the chicken to a platter and stir the parsley into the sauce. Pour the sauce over the chicken and garnish with more parsley.