Pound each of the 4 pieces of pork with the flat side of a meat mallet or a rolling pin. I find it cleaner to place the pieces, one at a time, into a gallon size plastic bag and pound. You are going for thin 1/4-inch cutlets. Pat dry with paper towels and lightly season both sides with salt and pepper.
Place the flour in a wide shallow bowl. Season the flour with salt and pepper. Whisk eggs in a second dish. Combine the panko breadcrumbs, dried oregano, and dried basil in a third dish. Also season with with salt and pepper.
One at a time, dredge cutlets in flour making sure to coat completely, shaking off excess. Next, dip into the eggs turning until all of the flour is coated, allowing excess to drip back into the dish. Lastly, press into the herbed breadcrumb mixture, turning to fully and evenly coat. Transfer to the prepares wire rack and baking sheet and let stand 15 minutes.
In a heavy skillet, preferably cast iron, heat 1/2 inch of oil over medium-high. When the oil shimmers carefully add two of the cutlets in a single layer, being careful NOT to crowd. Fry, flipping once, until golden brown all over and just cooked through, 4 to 5 minutes total. Transfer back to the prepared baking sheet lined with the wire rack. Let stand while you repeat repeat with remaining cutlets, at least 5 to 10 minutes more.
Preheat oven broiler with a rack about 8 to 10 inches from the heat element. Top cutlets evenly with Parmigiano-Reggiano, then tomato sauce, then a single slice of mozzarella. Broil just until cheese melts, 2 to 4 minutes. Top with basil and serve warm, with more tomato sauce and Parmigiano-Reggiano alongside.