1.5 pounds boneless, skinless chicken breasts – sliced into 4 cutlets and pounded 0.25 inch thick
1.25 teaspoons kosher salt
0.75 teaspoons black pepper – freshly ground
0.5 cup all-purpose flour
2 tablespoons extra-virgin olive oil
4 tablespoons unsalted butter
0.5 cup dry white wine
0.75 cup low-sodium chicken broth
2 tablespoons capers – rinsed
2 tablespoons flat-leaf parsley – finely chopped
Instructions
Juice the lemons to yield about 0.25 cup and set the juice aside; discard seeds, 3–5 minutes.
Prepare the chicken breasts: cut into 4 even cutlets, pound to 0.25 inch thickness, pat dry, then season both sides with the kosher salt and black pepper, 5–7 minutes.
Place the all-purpose flour in a shallow dish and dredge the cutlets, shaking off the excess so only a thin, even coating remains, 2–3 minutes.
Heat the extra-virgin olive oil and 2 tablespoons of the unsalted butter in a large skillet over medium-high heat until the butter foams, 1–2 minutes. Sear the cutlets until golden and just cooked through, 2–3 minutes per side; transfer to a warm plate and tent loosely with foil. Reserve the remaining 2 tablespoons butter for finishing.
Pour in the dry white wine, scraping up browned bits, and simmer to reduce by about half, 2–3 minutes. Add the low-sodium chicken broth and simmer until the sauce looks slightly syrupy and coats the back of a spoon, 3–4 minutes.
Stir in the reserved lemon juice and the capers; simmer to marry flavors, 1 minute. Return the cutlets and any juices to the pan and heat through, turning once, 1–2 minutes. Remove from heat, swirl in the reserved butter and the flat-leaf parsley until glossy, then taste and adjust seasoning as needed. Serve hot, spooning sauce over the cutlets.