Mix flour, Parmesan, salt, and pepper on a large plate. Slice each chicken breast into 3 thin cutlets. Place between plastic wrap and pound to about ¼ inch thick. Pat dry, then dredge each piece in the flour mixture. Shake off excess.
2 large chicken breasts, Salt and pepper, ½ cup all-purpose flour, ¼ cup finely grated Parmesan cheese
Heat olive oil and butter in a large skillet over medium-high heat. Sear the chicken in batches for 3–4 minutes per side, until golden and cooked through. Add more oil if needed. Transfer to a plate and turn off the heat.
3 tablespoons olive oil, 1 tablespoon salted butter
Wipe out most of the oil, but leave the browned bits in the pan. Add white wine and garlic. Simmer over medium heat for 4–5 minutes until reduced, scraping the bottom of the pan. Stir in capers, chicken broth, and lemon juice.
½ cup dry white wine, 4 garlic cloves, 2 tablespoons capers, 1 cup chicken broth, 2 tablespoons lemon juice
Return the chicken and any juices to the pan. Spoon sauce over the top. Cover partially and simmer for 3–5 minutes until the sauce slightly thickens.
Lower the heat, add cold butter, and swirl the pan until melted and glossy. Spoon the sauce over the chicken once more.
2 tablespoons cold salted butter
Remove from heat, sprinkle with chopped parsley, and serve warm.
¼ cup fresh parsley