Prep the chicken: Slice each chicken breast horizontally to make thin cutlets. Pat dry with paper towels. Season both sides generously with salt and pepper.

Dredge lightly: Place the flour on a plate. Dredge each cutlet in flour, shaking off the excess. You want a thin, even coating.

Sear the chicken: Heat a large skillet over medium-high heat. Add the olive oil and 1 tablespoon butter. When shimmering, add the chicken in a single layer. Cook 3–4 minutes per side until golden and just cooked through. Transfer to a plate and tent loosely with foil. Repeat with remaining cutlets if needed.

Sauté the aromatics: Reduce heat to medium. Add 1 tablespoon butter to the pan. Stir in the garlic and cook 30 seconds until fragrant. Avoid browning the garlic.

Deglaze the pan: Add the wine (if using). Scrape up browned bits with a wooden spoon. Let it bubble for 1–2 minutes until slightly reduced.

Build the sauce: Pour in the chicken stock, lemon juice, and lemon zest. Add the capers and a pinch of red pepper flakes if you like. Simmer 3–5 minutes, stirring, until the sauce reduces a bit and tastes bright and savory.

Finish with butter: Reduce heat to low. Swirl in the remaining 2 tablespoons butter until the sauce looks glossy and slightly thickened. Taste and adjust seasoning with salt and pepper.

Return the chicken: Nestle the cutlets back into the skillet, along with any juices on the plate. Spoon sauce over the top and simmer 1–2 minutes to warm through.

Garnish and serve: Sprinkle with chopped parsley. Add lemon slices if you want a pop of color. Serve immediately over pasta, rice, or mashed potatoes with extra sauce and lemon wedges.