This is the lightest of the cutlet recipes, with the bright, acidic lemon juice perfectly complemented by the briny capers and the fresh parsley. Be sure to keep your dusting of flour light; you’re not making a thick egg-and-bread-crumb coating.
Sprinkle the Chicken with the salt and pepper. Dredge the chicken in the flour to coat lightly. In a large sauté pan, melt 2 tablespoons of the butter with the 2 tablespoons of oil over medium-high heat. Add the chicken and cook just until brown, about 3 minutes per side. Using tongs, transfer the chicken to a plate.
Add the broth, lemon juice, and capers to the same pan. Bring the broth mixture to a boil over medium-high heat, scraping up the brown bits from the bottom of the pan for extra flavor. Return the chicken to the pan and simmer until just cooked through, about 5 minutes. Using tongs, transfer the chicken to a platter. Whisk the remaining 2 tablespoons of butter into the sauce. Pour the sauce over the chicken, garnish with the parsley, and serve.