Prepare the Chicken: Slice each chicken breast in half lengthwise to create four thinner cutlets. Season both sides with salt, pepper, and garlic powder. Dredge each piece in flour, shaking off any excess.
Cook the Chicken: Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Once hot, add the chicken cutlets and cook for 4-5 minutes per side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
Make the Sauce: In the same skillet, add the chicken broth, lemon juice, and lemon zest. Bring to a simmer, scraping up any browned bits from the bottom of the pan. Let the sauce reduce slightly, about 2 minutes. Stir in the remaining 2 tablespoons of butter until melted and the sauce is smooth.
Combine and Serve: Return the chicken to the skillet, spooning the sauce over each piece. Allow the chicken to warm through for about 2 minutes. Garnish with chopped fresh parsley, if desired, and serve immediately.