Using a meat mallet or a fork, tenderize the the pork. (If using a fork, see video for details)
*Optional* Combine the pork with the BRINE ingredients and allow to brine overnight. On the day of cooking, rinse the pork, and dry it thoroughly.
Cut the bread into cubes and place into a food processor. Pulse until you get crumbs a little larger than standard panko crumb size.
Coat the pork katsu in flour on both sides, and shake off the excess. Add the katsu into the egg and coat both sides. Dredge the pork again by repeating this step.
Add the pork into the panko bread crumbs and cover it completely. Lightly press the crumbs onto the pork, then place the katsu aside. Repeat with the remaining katsu.
In a large pot, heat cooking oil to 340F. When you add the katsu, the temperature will drop. Adjust the heat to bring the oil to a stable 325F. As the oil is heating up, allow the katsu to cook for 2 - 3 minutes, then flip. Cook for another 2 - 3 minutes, then remove to a draining rack and allow to cool.
On two slices of bread, spread mayonnaise, and my homemade tonkatsu sauce.
Pour homemade tonkatsu sauce on top of the pork katsu on both sides.
Place the katsu on the bread, top with sliced cucumber, and assemble the sandwich.
Slice into thirds, then repeat with the second sandwich. Serve with extra homemade tonkatsu sauce on the side.