Place chicken breasts between two sheets of parchment or plastic wrap and pound to about ½ inch thick. This ensures even cooking and a tender bite. Season lightly with salt and pepper on both sides before breading.
Set up a dredging station: one bowl with flour, one with beaten eggs, and one with panko breadcrumbs. Coat each chicken breast in flour, dip in egg, then press into breadcrumbs for full coverage.
Heat olive oil in a large skillet over medium heat. Fry the breaded cutlets until golden brown, about 3–4 minutes per side. Transfer to a plate lined with paper towels to drain excess oil.
In a small saucepan, melt butter over medium heat. Add minced garlic and sauté until fragrant. Stir in capers and lemon juice, then remove from heat and mix in chopped parsley.
Place cooked chicken on a serving platter and spoon the warm caper butter evenly over each cutlet. Garnish with extra parsley for a fresh, colorful presentation. Serve immediately for best results.