Preheat the oven to 425°F. Place a rimmed baking sheet in the oven while it preheats.
Cut the chicken breasts in half horizontally into even, thin pieces. Sprinkle both sides lightly with salt and pepper.
Create a dredging station: Place the flour in one shallow dish, whisk the eggs in a separate shallow dish, and combine the breadcrumbs, Parmesan, and lemon zest in a third.
Dredge the chicken in the flour, followed by the egg, and then the panko, pressing gently to adhere. Place the chicken pieces on a baking sheet.
Remove the hot pan from the oven and coat with cooking spray. Add the chicken to the hot pan and coat the tops of the chicken with more cooking spray. Bake for 15 to 20 minutes, turning halfway through, until the chicken is browned, crispy, and cooked through.
Meanwhile, whisk together the lemon juice, garlic, honey, mustard, and olive oil in a small bowl. Pour over the arugula, and toss just before serving.
To serve, place a chicken cutlet on a serving plate and top with the arugula. Shave Parmesan over the salad and serve.