Prepare the breading. Place 2 cups panko in a pie plate, add 1/2 teaspoon of the kosher salt, and stir with a fork to combine. Beat 3 large eggs in a second shallow bowl with the fork until evenly combined. Place 1/2 cup all-purpose flour on a plate.
Slice the chicken. Cut the tenders from 2 chicken breasts if still attached. Positioning a knife almost parallel to the cutting board, slice each breast crosswise at an angle into pieces about 1/3-inch thick. The pieces will not all be the same size, and that’s okay.
Season the chicken. Place the chicken, including the tenders, on a baking sheet. Season on both sides with the remaining 1 teaspoon kosher salt.
Dredge the chicken. Working with one piece of chicken at a time, dredge completely in the flour, then dip into the eggs, and finally thoroughly coat with the panko. Place back on the baking sheet in a single layer. Refrigerate while you heat the oil.
Heat the oil. Heat 3 cups vegetable oil in a large frying pan or cast iron skillet over medium-high heat until 350ºF, about 10 minutes. Meanwhile, fit a wire rack over a baking sheet. Make the sauce while the oil is heating.
Make the sauce. Place 1/2 cup ketchup, 1/4 cup Worcestershire sauce, 1 tablespoon soy sauce, 1 1/2 teaspoons granulated sugar, and 1 teaspoon apple cider vinegar in a small serving bowl and whisk to combine to make the sauce; set aside.
Fry the chicken. Fry the chicken in batches of about 5 pieces to prevent crowding: Add the chicken and fry, flipping once with tongs, until cooked through and golden-brown, 1 to 1 1/2 minutes per side. Transfer to the wire rack and repeat with the remaining chicken.
Slice the katsu and serve. If desired, slice the katsu crosswise into 1/2-inch wide pieces. Serve drizzled with the katsu sauce or serve the sauce on the side for dipping.
