Slice your chicken breasts horizontally to create 4 thin cutlets. Place each one between two pieces of plastic wrap and gently pound with a meat mallet until they're about 1/4 inch thick. Don't go crazy—you're aiming for even thickness, not paper-thin. Pat them dry with paper towels and set aside on a plate.

Mix your flour, salt, pepper, and paprika in a shallow bowl. This is your coating station. Dredge each chicken cutlet in the flour mixture, shaking off any excess. You want a light, even coating that'll turn golden when it hits the pan. Set the coated cutlets on a clean plate.

Heat your olive oil and butter together in a large skillet over medium-high heat. When the butter foams and you hear it sizzle, you know you're ready to go. This is the critical moment—don't skip the butter because it's what gives you that gorgeous golden crust and rich flavor.

Carefully place your chicken cutlets into the hot pan. You'll hear them sizzle immediately—that's exactly what you want. Cook for 3-4 minutes on the first side until golden brown, then flip gently and cook another 3-4 minutes on the other side. Don't move them around or you'll mess up that crust.

Remove the cooked chicken to a clean plate and tent it loosely with foil. Pour off most of the oil from the pan, leaving just a thin layer. Add your chicken broth and lemon juice to the pan and scrape up all those browned bits stuck to the bottom—that's pure flavor right there.

Stir in your capers and let the sauce simmer for about 2 minutes until it's slightly reduced. When your kitchen smells warm and buttery with that sharp caper tang cutting through, you'll know it's perfect. Taste it and adjust the lemon or salt as needed—this is your moment to make it exactly how you like it.

Return the chicken to the pan and spoon that gorgeous sauce over top. Let everything warm through for about 1 minute, then plate it up. Finish with fresh parsley and a sprinkle of Parmesan cheese right before serving.