In a shallow bowl, combine egg, Dijon mustard, garlic salt, salt and pepper and stir, then add chicken and let marinate for 1/2 an hour, or up to overnight in the refrigerator covered in plastic wrap.
In another shallow bowl combine panko bread crumbs and pinch of salt and pepper.
Pour 2 tablespoons vegetable oil into a large skillet over high heat for 1 minute.
Dredge chicken through bread crumb mixture and pat on breadcrumbs to make sure both sides are covered, then put into the heated oil in the skillet. Repeat with chicken, adding it to the skillet to fry (do not over-crowd the skillet, fry the chicken in batches if you need to.) Turn the heat down to medium-high, and cook for 3-4 minutes until a golden brown crust forms, then flip the chicken and cook for another 3 minutes, until cooked through and golden brown.
Remove chicken from skillet and put on a place on a plate until all the chicken is done cooking.
To assemble the salads, put 1 1/2 to 2 cups arugula in a bowl, sprinkle 1/8-1/4 of a cup (2 generous pinches) of shaved Parmesan cheese on top of the arugula, squeeze one lemon wedge over the salad, and place one lemon wedge on the side of the plate and place one chicken breast on top and serve!