Pork Katsu with Quick Carrot Pickles

Whisk together vinegar, water, sugar, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a large bowl. Using a vegetable peeler, shave as many ribbons as possible from carrots. Toss carrots and scallions with dressing. Lightly beat egg in a shallow bowl. Combine panko, 1/4 teaspoon salt, and 1/8 teaspoon pepper on a large plate. Pound pork chops to 1/8 inch thick between 2 sheets of plastic wrap with flat side of a meat pounder or with a rolling pin. Season both sides with 1/8 teaspoon each of salt and pepper (total). Coat with egg, letting excess drip off, then with panko, pressing to help adhere. Heat 3 tablespoons oil in a 12-inch heavy skillet over medium-high heat until it shimmers. Cook chops (in batches if necessary), turning once, until golden and just cooked through, 4 to 5 minutes total, adding remaining tablespoon oil if necessary. Drain briefly on paper towels and serve with carrot pickles.