Prepare the Chicken
Slice each chicken breast in half horizontally, making two thin chicken cutlets per breast.
Place between plastic wrap and gently pound to an even ½-inch thickness using a meat mallet or rolling pin.
Season both sides with salt and pepper.
Lightly dredge in flour, shaking off the excess.
Pan-Fry the Chicken
Heat olive oil and butter in a large skillet over medium-high heat.
Add the chicken (in batches if needed).
Cook for 3–4 minutes per side, until golden brown and crisp.
Transfer to a plate and tent with foil to keep warm.
Deglaze and Make the Sauce
Pour in the white wine, scraping up the brown bits with a wooden spoon.
Simmer for about 2 minutes to cook off the alcohol.
Add chicken broth, lemon juice, and capers.
Let it bubble for 2–3 minutes until slightly reduced.
Finish the Sauce
Whisk in butter, one piece at a time, until melted and glossy.
For thicker sauce, sprinkle in flour while whisking.
Taste and adjust with extra lemon, butter, or salt as needed.
Combine and Serve
Return chicken cutlets to the pan, spooning sauce over them.
Simmer 1–2 minutes until heated through.
Garnish with fresh parsley and lemon slices.
Serve hot over pasta, rice, or potatoes.