Begin preparing the chicken by cutting the chicken breasts in half horizontally. Place each breast on a cutting board with the thick end facing the direction you will be cutting. If desired, remove the tender and set aside. Firmly press down on the chicken while keeping your fingers up and away from the knife. Use a sharp chef's knife to slice down the middle of the chicken breast separating it into two equal pieces. Repeat with the remaining chicken.
Flatten the chicken breasts and tenders so that they are relatively even in size. Cover each piece of chicken with a piece of cling film and gently pound with a mallet or heavy rolling pin until the piece is roughly even in thickeness. Set chicken aside.
Set up your breading station. In a shallow dish add the flour along with a big sprinkle of kosher salt. In another shallow dish add the eggs, water and a good spinkle of kosher salt and whisk together until the egg is well mixed. Lastly combine the panko bread crumbs, grated parmesan cheese, dried basil, and dried oregano in a third shallow dish and whisk together.
Bread the chicken cutlets. Place a piece of chicken in the flour, flipping it over to cover completely. Lift the chicken up and shake off the excess flour. Place the floured chicken cutlet in the egg mixture, flipping over to completely coat the chicken in egg. List the chicken up and let the excess egg drip off. Lay the the cutlet onto the crumb mixture. Spread the crumbs over the top and gently press down to help the crumbs adhere. Lift the cutlet off and very gently shake off the excess. Transfer the breaded chicken to a parchment lined baking sheet.
Preheat the oven to 300°F / 150°C. Heat up a quarter inch of vegetable oil in a wide skillet over medium low heat. Set up a draining station by lining a baking sheet either with a rack or paper towels to absorb the oil. A good trick for determining when the oil is ready to toss a small piece of bread crust into the oil. When the bread is bubbling and lightly brown then the oil is ready to go.
To cook the chicken, carefully lay 2 or 3 pieces of chicken into the hot oil. Let cook for 3 to 4 minutes until the bottom is golden brown. Carefully flip the chicken over and cook for another 3 to 4 minutes until both sides are golden brown. When browned lift the chicken out of the oil letting the excess drip off before transferring them to the rack or paper towel lined baking sheet. Lightly sprinkle each cutlet with a pinch of kosher immediately after removing from the cooking oil; this will help the salt to adhere to the crust. Transfer the baking sheet to the oven to keep warm while you pan fry the remaining pieces.
While the chicken is cooking prepare the arugula salad. In a salad bowl, squeeze the juice from half a lemon. Add a pinch of kosher salt and pepper and whisk together. While whisking, slowly drizzle in the olive oil. Add the arugula and toss with the vinaigrette. Set aside until the chicken is finished cooking.
To serve, plate one or two chicken cutlets on each plate, top with a pile of the dressed arugula and lots of freshly shaved parmesan cheese!