Cut the chicken: Slice the chicken breasts in half horizontally.
Coat the chicken: Mix flour, parmesan, salt, and pepper in a shallow bowl or dish. Dredge the chicken in the mixture, coating both sides.
Cook the chicken: Heat the oil and butter in a large skillet over medium-high heat. Sear the chicken for 3 to 4 minutes per side, until cooked through with a golden crust. Use tongs to remove the chicken to a plate.
Make the sauce: Add the wine and garlic to the pan, letting it simmer for 3 to 4 minutes, until reduced by about half. Then add the broth, lemon juice, capers, and butter, stirring until it begins to simmer again.
Add the chicken: Add the chicken back to the pan. Spoon the sauce on top and let it simmer for 1 to 2 minutes, until warmed through.
Serve: Garnish with parsley before serving.
Notes
Instead of slicing the chicken breasts in half, you have the option to buy four smaller chicken breasts and flatten them to a thinner consistency using a kitchen mallet.