These thin chicken cutlets take about 5 minutes to cook and make for a hearty match to crisp arugula and curls of parmigiano-reggiano cheese.
Divide arugula among 4 plates, leaving center of each empty; season with salt and pepper. Season chicken on both sides with salt and pepper. Heat 1 tablespoon oil in a large, heavy skillet over medium-high. Working in batches so as not to crowd, place cutlets in pan and cook until golden brown on bottom, about 2 minutes. Flip and continue to cook until completely cooked through, 2 to 3 minutes. Transfer to plates, next to arugula. Wipe out pan and repeat with remaining oil and chicken. Drizzle with oil, scatter with cheese, and serve, with lemon wedges.