Place individual chicken strips between layers of parchment paper and pound them into ¼-½ inch thick slices using a meat tenderizer. Sprinkle chicken with a big pinch of kosher salt on both sides; set aside for now.
In a shallow bowl, combine flour, Italian seasoning, garlic powder, kosher salt, and black pepper and whisk to combine. In another bowl, add the panko, pecorino, and parmesan, whisk to combine. In a third bowl, crack the eggs and whisk until the eggs are airy and light.
Dunk the chicken in the flour mixture, press to coat, shake off excess. Then place cutlet in the egg wash and make sure no dry bits remain. Transfer to panko mixture. Press the cutlet down so the breading adheres. Place cutlets on a clean plate. Continue dredging the same way.
Heat avocado oil in a sauté pan or a skillet over medium-high heat. Check to see if the oil is hot by dropping a panko crumb. It should sizzle immediately.
Fry the cutlets in small batches (2-3 pieces at a time) for 3-5 minutes total, flipping the chicken around the halfway mark until golden brown. Remove to a wire rack placed on a baking sheet. Continue cooking remaining cutlets the same way. Add more oil if needed.
Combine olive oil, dijon, lemon juice, honey, a big pinch of salt, and freshly cracked pepper in a mason jar with a lid. Shake until mixed. In a salad bowl, add arugula, onions, apple and toss in a couple tablespoons of the dressing. Taste and add more dressing as desired. Top with shredded parmesan.
Place cutlets on plate and top with the prepared salad or serve on the side immediately.