Slice each chicken breast in half horizontally to create thinner cutlets.
Place each piece of chicken between 2 pieces of parchment paper or plastic wrap. Use a rolling pin or meat mallet to pound the chicken flat for even cooking.
Sprinkle each piece of chicken with salt and pepper to taste.
Prepare 3 dishes for breading the chicken. Place the flour in the first dish. In the second dish, whisk together the eggs and milk, and season with a pinch of salt and pepper.
In the third dish, mix together the Panko breadcrumbs, Parmesan cheese, kosher salt, and ground black pepper.
Dip each piece of chicken into each of the 3 dishes to dredge and fully coat in breadcrumbs.
Heat 3 tablespoons of olive oil or butter in a large skillet over medium heat. Once heated, place two pieces of breaded chicken in the pan.
Cook on each side for about 2 minutes or until the breading is golden brown and crispy, and the chicken is cooked through.
Add more olive oil or butter to the skillet and pan fry the remaining chicken breasts.
In a bowl, whisk together the olive oil, lemon juice, garlic, salt, and pepper.
Add in the arugula and toss to coat.
Serve the salad on plates, topping each serving with shaved Parmesan cheese. Place the chicken breasts on top or alongside the salad. Serve with lemon wedges.
