Prep the chicken: Place each cutlet between sheets of plastic wrap and pound to about 1/4-inch thickness. Pat dry. Season both sides with salt and pepper. Lightly dredge in flour, shaking off excess.

Sear the cutlets: Heat olive oil and 1 tablespoon butter in a large skillet over medium-high. When hot and shimmering, add cutlets in a single layer (work in batches). Cook 2–3 minutes per side until golden and just cooked through. Transfer to a plate; tent loosely with foil.

Build the fond: Lower heat to medium. Add garlic and sauté 20–30 seconds until fragrant, scraping up browned bits. Do not let it burn.

Deglaze: Pour in white wine. Simmer 1–2 minutes, scraping the skillet, until the wine reduces by about half.

Make the sauce: Add chicken broth, lemon juice, and capers. Simmer 3–4 minutes until slightly reduced. Taste and adjust salt and pepper. For extra lemon aroma, stir in a pinch of zest.

Finish with butter: Off the heat, whisk in the remaining 1 tablespoon cold butter until the sauce looks glossy.

Return chicken: Nestle cutlets and any juices back into the skillet. Spoon sauce over the top and warm for 1 minute.

Garnish and serve: Sprinkle with parsley. Add lemon slices if you like. Serve immediately over pasta, potatoes, rice, or sautéed greens.