Prepare the chicken: Place each chicken breast between two pieces of plastic wrap and pound to an even 1/2-inch thickness using a meat mallet or rolling pin.

Season the flour: In a shallow dish, mix the flour, salt, and black pepper. Dredge each chicken breast in the flour mixture, shaking off any excess.

Cook the chicken: Heat 2 tablespoons of butter and olive oil in a large skillet over medium-high heat. Add the chicken and cook for 3-4 minutes per side until golden brown and cooked through. Remove and set aside.

Make the sauce: In the same skillet, add the chicken broth, white wine, and lemon juice. Bring to a simmer, scraping up any browned bits from the bottom of the pan.

Finish the sauce: Stir in the capers and remaining 2 tablespoons of butter until the sauce thickens slightly, about 2-3 minutes.

Serve: Return the chicken to the skillet and coat with the sauce. Garnish with chopped parsley and lemon slices before serving.