The first step in making Chicken Piccata is preparing the chicken breasts. You'll want to start by slicing each chicken breast in half horizontally to create two thin cutlets. Then, place each cutlet between two sheets of plastic wrap and pound them with a meat mallet or the bottom of a heavy skillet until they're about 1/4 inch thick. This will help them cook quickly and evenly.

After pounding the chicken, you'll want to dredge them in a mixture of flour, salt, and pepper. This will help create a crispy outer layer and also thicken the sauce later on. To do this, spread the flour mixture on a shallow dish and coat each chicken cutlet on both sides, shaking off any excess flour.

Once the chicken cutlets are coated in flour, it's time to cook them. Heat 1/4 cup of butter and 2 tablespoons of olive oil in a large skillet over medium-high heat until the butter is melted and foamy. Add the chicken cutlets to the pan and cook them for about 3-4 minutes on each side, or until golden brown and cooked through. Remove the chicken cutlets from the pan and place them on a plate.

The next step is to make the sauce for the Chicken Piccata. In the same pan used to cook the chicken, add 3/4 cup of dry white wine and 1/4 cup of fresh lemon juice. Cook the mixture over medium-high heat until it's reduced by half, stirring occasionally. Add 1/4 cup of chicken broth and 2 tablespoons of capers, and continue cooking the sauce for another 2-3 minutes until it thickens slightly.

To finish the Chicken Piccata, add the chicken cutlets back to the pan and spoon the sauce over them. Cook for another minute or two, until the chicken is heated through and the sauce has thickened to your desired consistency. Remove the pan from the heat and stir in 1/4 cup of butter until it's melted and incorporated into the sauce.