Begin by prepping the eggplant. Trim a thin slice of skin off the eggplant on either side. Cut each eggplant into 4 slices half an inch thick. Line a baking sheet with paper towel. Liberally sprinkle both sides of the eggplant slices with kosher salt and place on the paper towel lined baking sheet.
Allow the eggplant slices to sit at room temperature for at least 30 minutes or up to 60 minutes. The salt will draw out excess moisture from the eggplant. Blot the eggplant dry on both sides with fresh paper towel and set 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 eggplant cutlets. Place a piece of eggplant in the flour, flipping it over to cover completely. Lift the eggplant up and shake off the excess flour. Place the floured eggplant cutlet in the egg mixture, flipping over to completely coat the cutlet. Lift the eggplant 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 eggplant 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 eggplant, carefully lay 2 or 3 pieces into the hot oil. Let cook for 3 to 4 minutes until the bottom is golden brown. Carefully flip the eggplant over and cook for another 3 to 4 minutes until both sides are golden brown. When browned lift the eggplant 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 eggplant 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 eggplant is finished cooking.
To serve, place one or two eggplant cutlets on each plate, top with a pile of the dressed arugula and lots of freshly shaved parmesan cheese!