Preheat oven to 425°F.
Line 3 large plates in a row and put the flour in the first, the beaten eggs in the middle and the panko breadcrumbs in the third. Add the red pepper flakes, garlic powder, dried basil, dried oregano, ½ teaspoon kosher salt and ⅛ teaspoon black pepper to the panko and mix well, ensuring all elements are combined.
Place the chicken breasts on a cutting board and cover with plastic wrap. Using a meat pounder, rolling pin or heavy-bottomed pan, pound the chicken until it is an even thickness and very thin, about ¼ inch thick. Season both sides of the chicken with salt and pepper.
Starting with the flour, dredge each chicken breast, allowing a light coating of flour to adhere to both sides. Next, coat each side of the chicken in the egg mixture, allowing any excess egg to drip off before placing the chicken in the breadcrumbs. Coat both sides of the chicken in the panko, ensuring an even, complete coating adheres. Transfer to a plate and set aside.
Warm ¼ inch of frying oil in a heavy-bottom skillet until very hot but not smoking. Carefully add the chicken to the pan and fry for 3 minutes per side, until browned and crisp, adjusting the heat as needed. Transfer the chicken to a plate lined with a paper towel, allowing any excess grease to drain off.
Place the bottom half of each roll on a baking sheet. Top with the chicken breasts and then layer the mozzarella cheese over each sandwich. Add the tomato slices and transfer to the oven. Bake for 3 minutes and then add the top of each roll to the baking sheet (not on top of the chicken). Cook for an additional 2–3 minutes, until the mozzarella has begun to bubble and melt over the chicken.
While the chicken is cooking, place the arugula and basil in a bowl and add the olive oil, balsamic vinegar, a pinch of kosher salt and a pinch of black pepper. Toss with your hands to make sure the salad is well dressed.
Remove the chicken from the oven and transfer to serving plates. Top with the arugula and basil salad and top with the other half of the roll before serving.