Start by placing your boneless, skinless chicken breast between two sheets of plastic wrap. Use a meat mallet or rolling pin to gently pound the chicken to an even thickness, about 1/2 inch.
Season both sides of the chicken with salt and black pepper.
Prepare three shallow bowls: one for the beaten egg, and one for the panko breadcrumbs.
Dip each piece of chicken into the beaten egg, allowing excess to drip off, then coat it generously with panko breadcrumbs.
In a deep frying pan or pot, heat enough oil for frying (about 1-2 inches deep) over medium-high heat.
Carefully add the breaded chicken cutlets to the pan, frying in batches if necessary. Fry for about 3-4 minutes on each side until golden brown.
In a small bowl, whisk together the ketchup, Worcestershire sauce, soy sauce, mirin, sugar, and Dijon mustard until smooth.
Slice the fried chicken cutlets into strips and serve them hot with a drizzle of the homemade sauce.