Setup the breading station. In a small, shallow container or bowl, combine 1 cup all-purpose flour with 2 tsp Kosher salt and ¼ tsp freshly ground black pepper. Whisk 2 eggs in a medium bowl to combine. Combine 1 cup panko, ½ cup Parmesan, 2 Tbsp chopped basil or parsley, and remaining 1 tsp salt in a separate dish.
Prepare the chicken cutlets. Dredge the chicken cutlets evenly on all sides with flour, then move the chicken to the eggs, turning to coat on all sides. Shake off any excess, then transfer the cutlets to the panko breadcrumbs mixture and coat evenly on all sides. Repeat with all chicken cutlets.
Cook the chicken. Heat a few tablespoons of grapeseed or vegetable oil over medium-high heat in a large skillet. The amount of oil will depend on the size of the pan you use--you need an even layer on the bottom of the pan that goes up approximately ⅛-¼-inch up the side. When oil is hot, transfer breaded chicken and cook for 3-4 minutes per side, until golden brown, but not burned. Move chicken to a wire rack to cool while you finish cooking.
Assemble the panini. Cut focaccia in half crosswise. Spread an even layer of pesto on both sides, then layer ingredients in the following order on the bottom slice: arugula, chicken cutlet, roasted red peppers, provolone cheese. Place the top on, then brush both sides with olive oil or melted butter.
Cook the panini. Heat a grill pan or panini press over medium heat. When hot, add panini, then press down with weight or heavy pan. Cook for 4 minutes, then flip (if not using a panini press that cooks both sides at the same time) and cook an additional 4 minutes.
Slice, then serve! Carefully transfer the panini to a cutting board, cut on the diagonal, then serve immediately.