Break egg into a bowl and whisk with a fork until well mixed.
Salt and pepper both sides of the pork chops.
Dunk each pork chop in the egg so that it is completely covered in egg. Once covered, press the pork chop into the panko, then flip and press the other side into the panko. You may need to use your hands to cover each chop with panko.
Heat a skillet and 1 tbsp of oil over high heat until very hot. Add pork chops into the oil and reduce heat to medium. Cook the pork chops for approximately 2 minutes. Use a spatula to lift them slightly and check that the panko has browned. If they have not thoroughly browned, let cook another 1-2 minutes until browned. Now flip, and repeat the process.
Once the sides are both nicely browned, flip them so the best browned side is face up in the skillet. There should not be much oil left in the skillet, most will have been absorbed by the panko. With a properly fitting lid in hand, add ¼ cup water to the pan and cover immediately. Be prepared to lower the heat in case the pan begins to spray, but the lid should allow the pan to only release steam.
Allow the skillet to cook while covered until the water is cooked off. You will notice the amount of steam reduces to nearly none, and you might smell fallen panko crumbs begin to burn. It should take about 3 minutes. At this point, remove the lid and use an instant read thermometer to check the temperature. If the pork has not reached your desired temperature, add another ⅛ cup of water and cover again. It should take another 3 minutes for the water to boil off again. Check the temperature again. If still not done, repeat the process, but mine were done after the first ⅛ cup of water had cooked off.
Remove the pork chops to a cutting board. You can serve them as they are, or slice thin and serve for easier eating. Enjoy :-)