Make the tonkatsu sauce by whisking together the tomato ketchup, Worcestershire sauce, brown sugar, oyster sauce, and mustard until smooth, then set aside.
Using a kitchen mallet or a heavy rolling pin, flatten the chicken thighs until they are roughly ½-inch thick.
Season both sides of the flattened chicken thighs, then thoroughly coat the meat in a layer of flour, shaking off any excess.
Dip the floured chicken thighs into the egg so it is thoroughly drenched.
Lastly, thoroughly coat each chicken thigh with the panko crumbs, shaking off any excess.
Heat up a deep fryer to 350 F. Alternatively, if you do not have a deep fryer you can heat up 1 ½ cups of frying oil in a medium or large frying pan.
Once the oil is at 350 F, add one chicken thigh at a time to the fryer and leave it to cook for 2 to 3 minutes, until it is crispy and golden. If cooking the chicken in a frying pan, cook it for 2 to 3 minutes on each side until golden and cooked through.
Remove the finished chicken from the fryer and set it on a kitchen towel to absorb any excess oil, while repeating the process with the remaining chicken thighs.
Serve the chicken katsu hot, with the tonkatsu sauce drizzled on top.