Begin by flattening the chicken breasts: Place each chicken breast between two pieces of plastic wrap and pound with a meat mallet until about 1/2 inch thick.
Season both sides of the chicken with salt and pepper. Dredge each piece lightly in flour, shaking off any excess.
In a large skillet, heat 2 tablespoons of butter and the olive oil over medium-high heat until the butter is melted and bubbly.
Add the chicken breasts to the skillet in a single layer. Cook for about 4-5 minutes on each side, or until golden brown and cooked through. Remove chicken from the skillet and keep warm.
In the same skillet, add minced garlic and sauté for about 30 seconds until fragrant.
Carefully add the chicken broth, lemon juice, and lemon zest, scraping the bottom of the pan to release any brown bits. Bring to a simmer.
Stir in the capers and allow the sauce to cook for another 2-3 minutes until slightly reduced.
Reduce the heat to low, and return the chicken to the skillet, spooning the sauce over the top. Add the remaining 2 tablespoons of butter for a rich finish.
Cook for an additional minute to warm the chicken through, ensuring it is well-coated in the sauce.
Serve the chicken piccata immediately, garnished with fresh parsley and extra lemon slices if desired.