Place chicken breasts between plastic wrap and pound with meat mallet until evenly flattened to about half-inch thickness.

Season both sides of chicken cutlets generously with salt and freshly ground black pepper.

Place flour in shallow dish and dredge each chicken cutlet thoroughly, shaking off excess flour.

Heat olive oil in large skillet over medium-high heat until shimmering.

Working in batches, add floured chicken cutlets to hot skillet and cook 3-4 minutes per side until golden brown and cooked through to 165°F.

Transfer cooked chicken to serving platter and tent loosely with foil to keep warm.

Add 2 tablespoons butter and minced garlic to same skillet and sauté 30 seconds until fragrant.

Pour in chicken broth and white wine if using, scraping up all browned bits from bottom of pan.

Add fresh lemon juice and capers to skillet, bringing mixture to gentle simmer.

Allow sauce to reduce by about half for 5-7 minutes until slightly thickened.

Remove skillet from heat and swirl in remaining 2 tablespoons cold butter until completely melted and sauce appears glossy.

Return chicken cutlets to skillet, spooning sauce over top and turning to coat evenly.

Transfer sauced chicken to serving platter, pour remaining pan sauce over top, and garnish with fresh chopped parsley before serving immediately.