Prepare the chicken: Place one piece of the chicken breast on a sheet of wax paper. Use one hand to press down on the chicken and, using a sharp knife, use your other hand to cut it in half horizontally. You should have two thinner pieces. Repeat with the other chicken breast. Working with one chicken cutlet at a time, place the chicken on a sheet of wax or parchment paper and top with another sheet of wax or parchment paper. Gently pound the chicken cutlet using a meat mallet or pounder or the bottom of a heavy skillet; pound the chicken to about ¼ to ½ inch thickness. Repeat with the remaining chicken cutlets. Season liberally with salt and pepper.
Place the eggs in a medium bowl and whisk with salt and pepper. Place the flour on a medium plate and season with salt and pepper. And finally, place the Panko or breadcrumbs on a medium plate.
Take one chicken cutlet at a time and dredge in the seasoned flour. Then dip it into the egg mixture and coat on both sides. Then dip it into the Panko, pressing lightly to make sure the breadcrumbs adhere. Place on a cookie sheet. The chicken can be prepared up to this point, covered and refrigerated, for several hours ahead of time.
Cook the chicken: preheat the oven to 225F degrees. Heat 2 tablespoons of the oil and half the butter in a large, heavy skillet over moderate heat until the butter begins to sizzle. Add the chicken, one or two cutlets at a time (you don’t want to crowd the skillet or the chicken won’t crisp up) and cook for about 4 to 6 minutes per side (depending on how thin/thick your cutlets are) or until golden brown and cooked through. If you want you can insert an instant thermometer; it should read 165F degrees in the thickest part of the chicken cutlet. Place on a plate and keep warm in the oven. Cook the remaining chicken using the remaining oil and butter as needed.
Meanwhile gently toss the arugula in a bowl with the oil, vinegar, salt, and pepper.
Serve the chicken topped with the arugula and then the Parmesan shavings and lemon wedges.

Braised chicken with leeks, artichokes, and spring herbs