Begin by slicing each chicken breast in half horizontally to create thinner cutlets. Place the chicken between two pieces of plastic wrap and gently pound them to an even thickness of about 1/2 inch.

In a shallow dish, combine the flour, salt, and black pepper. Dredge each chicken cutlet in the flour mixture, shaking off any excess.

In a large skillet, heat the olive oil and 1 tablespoon of butter over medium-high heat. Once hot, add the chicken cutlets and cook for about 3-4 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.

In the same skillet, add the chicken broth, lemon juice, and capers. Bring to a simmer, scraping up any browned bits from the bottom of the pan. Let it cook for about 2-3 minutes to reduce slightly.

Return the chicken to the skillet and cook for an additional 1-2 minutes, spooning the sauce over the cutlets. Remove from heat and stir in the remaining tablespoon of butter until melted.

Serve the chicken piccata hot, garnished with fresh parsley and accompanied by the sauce from the skillet.