Butterfly the chicken breasts and pound them thin until even.
Set up three dredging stations: flour, eggs mixed with grated Parmigiano, and a mixture of plain breadcrumbs and panko. Season each with salt and pepper.
Dredge the chicken in flour, then egg, then breadcrumbs, pressing firmly so the coating adheres.
Heat about ½ inch of oil in a skillet over medium-high heat.
Fry the chicken cutlets for 3–4 minutes per side, until golden brown and crisp.
Transfer to paper towels to drain.
In a bowl, whisk together lemon juice, olive oil, salt, and pepper.
Toss with the arugula until lightly dressed.
Plate the chicken cutlets with the arugula salad on top or alongside, and serve with lemon cheeks.
