Slice each chicken breast in half horizontally. 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. Sprinkle each piece of chicken with salt.

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 the mixture with a pinch of salt and pepper. In the third dish, whisk together the breadcrumbs, parmesan cheese, salt, and pepper.

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 the bottom of a bowl, whisk together the olive oil, lemon juice, garlic salt, and pepper. Add in the arugula and toss to coat. Add a portion of salad to each plate. Top each salad serving with shaved parmesan cheese. Place the chicken breasts on top of or alongside the salad. Serve with lemon wedges.