Cut cabbage into thin strips in advance to serve as a side.
Make several slits along the border between the lean and fatty parts of the pork with the tip of a knife.
Pound the pork with a meat tenderizer or the back of a knife to even out its thickness. Sprinkle salt and pepper on both sides.
Crack egg into a bowl and beat it. Prepare three containers and place flour, the beaten egg, and panko breadcrumbs in each one separately.
Coat both sides of the pork in this order: flour, beaten egg, and panko breadcrumbs. When applying the flour, gently shake off any excess with your hands. After coating the pork, let it sit for about 10 minutes to allow the breading to set.
Heat oil in a pot to 340℉ (170℃). If you don't have a thermometer, drop a few panko breadcrumbs into the oil to test the temperature. When the breadcrumbs float to the surface at a moderate pace (not too quickly and not too slowly), it indicates that the oil is ready.
Carefully place each piece of pork into the oil one at a time and deep-fry for about 1-2 minutes. Then, flip each piece over when the breading becomes slightly browned. Continue cooking until they are browned all over and the bubbles floating on the oil surface become smaller, which takes about 3-4 minutes. The total deep-frying time should be around 4-6 minutes (depending on the thickness of the pork).
Remove the pork from the pot and place it upright on a wire rack or paper towels to drain excess oil. Let it rest for 3-5 minutes to lock in the juices.
Cut the pork into ⅘-inch (2cm) slices.
Serve the pork slices on plates with the shredded cabbage on the side. Pour tonkatsu sauce over the pork to taste.