Begin by slicing each chicken breast in half horizontally to create thinner cutlets. Place the chicken between two sheets of plastic wrap and gently pound with a meat mallet until about 1/2 inch thick.

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.

Return the chicken to the skillet and cook for an additional 2 minutes, allowing the flavors to meld. Remove the chicken from the skillet again and place on a serving platter.

Stir in the remaining tablespoon of butter into the sauce until melted and smooth. Pour the sauce over the chicken and garnish with fresh parsley before serving.