Slice the 10 oz chicken breast horizontally to make two even cutlets; season both sides with 1/2 teaspoon salt and 3 dashes black pepper and let sit for 10 minutes.
In a small bowl, whisk together 1 1/2 tbsp ketchup, 2 tbsp Worcestershire sauce, 1 tbsp soy sauce, 1 tbsp mirin, 1 tbsp sugar, and 1/2 tsp Dijon mustard until smooth; set aside as katsu sauce.
Pour oil into a deep pot to a depth suitable for deep-frying and heat to about 350°F (180°C).
Prepare a breading station: beaten egg in one shallow bowl and 1 cup panko in another.
Dip each seasoned chicken piece into the beaten egg, then press into panko to coat; for a thicker crust, dip again in egg and recoat with panko.
Carefully lower the breaded chicken into the hot oil and deep-fry until golden brown on both sides, about 3–4 minutes total per piece (cook time may vary by thickness).
Remove chicken to a paper-towel-lined plate to drain, then slice into strips and serve immediately with steamed rice and the prepared katsu sauce.
