Similar to chicken piccata, this recipe is easy yet delicious. “Paillard” is a French technique of pounding meat flat before cooking. It works well for chicken breasts because they become tender and cook more quickly, before they get a chance to dry out. (Bonus: more surface area to drench with a delicious lemon-caper sauce.)
Prepare chicken breasts: Lay the chicken between two large sheets of plastic wrap. With a meat mallet or heavy sauté pan, pound each breast to a ½-inch thickness. Salt each breast liberally, sprinkling from a height to ensure even distribution, then season with pepper. Flip each breast and season the other side. If using mustard and tarragon, spread about 2 teaspoons of mustard and 1 tablespoon chopped tarragon leaves on one side of each breast.Spread flour onto a dinner plate. Dredge breasts by coating them completely with flour, then shake off any excess. (They should be lightly dusted.) Set aside. Repeat with remaining breasts.
Pan-fry chicken: Place skillet over high heat. While it’s heating, trim, halve, and peel the shallot. When the skillet begins to smoke, add oil. When the oil begins smoking, gently place the chicken breasts in the pan in an even layer, so that they do not overlap. (You may need to work in batches if your skillet is smaller.) Allow them to cook undisturbed until they are nicely browned on the first side, about 3 minutes. Do not move the chicken around while it cooks, or the crust will stick to the pan. Meanwhile, mince the shallot.After the first side is browned, flip the breasts and finish cooking, 2–3 minutes. (Depending on the strength of your range, you may need to turn the heat down so the flour doesn’t burn.) When they are just cooked through and have only a little give when pressed with a finger, 6–8 minutes total, transfer them to a wire rack over a rimmed baking sheet.
Lower the heat to medium. Add the minced shallot and stir with a wooden spatula. Add the lemon wheels and a pinch of salt; stir, but do not flip the lemons (they’ll caramelize better if left to cook on one side). Scrape up any bits of flour and fat at the bottom of the pan. Once the shallots are caramelized and the lemons have begun to brown, about 2–3 minutes, add the wine and stir. When about half the wine has cooked off, turn the heat to high. Add the butter to the pan one tablespoon at a time, shaking and moving the pan continuously until all the butter has melted and emulsified into the sauce. Add the capers, stir, and remove pan from heat. Transfer chicken to a platter, then spoon the sauce over each breast. Arrange lemon wheels on top and serve immediately.