Prep the chicken: Butterfly the chicken breasts and cut into thin cutlets. Pat dry.
In a shallow dish, mix flour, salt, pepper, and garlic powder. Dredge each cutlet lightly, shaking off excess.
Sear in batches: Heat 1 tablespoon olive oil in a large skillet over medium to medium-high heat. Add two cutlets and cook until golden, about 3 minutes per side.
Transfer to a plate and repeat with remaining oil and chicken.
Sweat the garlic: Reduce heat to medium. Add butter to the skillet. Once melted, add minced garlic and cook 30 seconds until fragrant, scraping up browned bits.
Deglaze: Pour in white wine.
Simmer 1–2 minutes, scraping the pan, until slightly reduced and no harsh alcohol smell remains.
Build the sauce: Add chicken broth, lemon zest, lemon juice, and capers. Bring to a gentle simmer. If you like a little heat, add a pinch of red pepper flakes.
Finish the chicken: Return the cutlets and any juices to the skillet.
Simmer 3–5 minutes, flipping once, until the sauce lightly thickens and the chicken reaches 165°F.
Adjust and serve: Taste the sauce and season with salt and pepper as needed. Stir in parsley. Serve with extra lemon slices and spoon sauce over the top.