Place the breadcrumbs in one bowl, the eggs in a second, and the flour in a third. Season each bowl with salt and pepper.
Dip the chicken first into the flour, then into the eggs, and lastly into the breadcrumbs and place on a baking sheet or large plate.
Preheat the oven to 350°F. Set a wire rack over a baking sheet.
Heat 1 inch of oil in a shallow skillet to 375°F. When hot, fry the breaded chicken until golden brown, turning once. Transfer to the prepared wire rack.
Top each piece of chicken with mozzarella and finish cooking in the oven until the chicken reaches an internal temperature of 165°F.
Meanwhile, make the sauce. Heat the olive oil in a small saucepan. Add the garlic and cook for 1 minute, until fragrant. Add the chile flakes and cook for 1 to 2 minutes. Stir in the crushed tomatoes and bring to a simmer. Stir in the basil and remove from the heat. Season with salt and pepper.
For the salad, in a blender or food processor, blend the basil, mayonnaise, both vinegars, garlic, sugar and salt. Slowly stream in the oil until emulsified. Adjust seasoning.
Toss the arugula with the salad dressing to coat fully.
Place a chicken breast on each hero sandwich bun, top with tomato sauce, arugula salad, parmesan and basil.