Step 1

Preheat oven to 200°F. Whisk together eggs and water in a shallow bowl. Stir together panko, grated cheese, and 1 teaspoon of the salt in separate shallow dish.

Step 2

Dry chicken well with paper towels. Place each chicken piece in egg mixture, turning to fully coat; allow excess to drip off. Transfer pieces to panko mixture, and turn to coat, pressing to adhere mixture.

Step 3

Melt 1 tablespoon butter with 2 tablespoons of the olive oil in a large skillet over medium-high. Add 2 chicken pieces to skillet, and cook until golden brown and internal temperature registers 160°F, 2 to 3 minutes per side. Transfer chicken to a wire rack set inside a rimmed baking sheet skillet. Season with 1/4 teaspoon of the salt, and keep warm in preheated oven. Repeat with remaining butter, chicken, 2 tablespoons of the oil, and 1/4 teaspoon of the salt.

Step 4

Toss together arugula, lemon juice, and remaining 1 tablespoon oil and 1/4 teaspoon salt. Garnish with shaved pecorino cheese. Divide chicken and salad among 4 serving plates, and serve immediately with lemon wedges.