Using a meat mallet or a rolling pin pound the meat until pretty thin, less than 1/4" thick. Be careful not to pound it to the point where it is falling apart. Pounding the meat will make the meat easier to stuff and fry and will make it much more tender, don't skip this step. I like to put some plastic wrap over the meat to prevent any flying bits and for easier clean up later.
Put a slice of ham and cheese on half of each piece of meat then overlap with the other half of meat and kind of tuck everything securely in and use toothpicks to further secure everything in so it doesn't open and leak out during the frying. Just be very careful later to remove all the toothpicks.
Prepare your dredging station. Beat the eggs with some salt and pepper and couple of tablespoons of milk. In another shallow bowl season the flour well with salt and pepper and finally in a third shallow bowl season the bread crumbs with garlic powder, salt and pepper.
The process is that you will first dip and cover the pork well in flour, then it will go into the eggs and after that into bread crumbs. I then like to take it back to the eggs and one more time into the bread crumbs. I don't always do this when frying, but since this is stuffed with cheese, I want to give it a bit thicker breading so nothing leaks out. If you are low on the egg mix just add another one in with a splash of milk and a bit more of salt and pepper.
Once you have all the pork breaded, carefully lower into the oil and fry until golden brown, about 6-8 minutes on each side. Transfer on a cooling rack for just a few minutes before serving. If you can, take toothpicks out before servings it, or make sure you pay attention to them while eating. This is the only part that makes me nervous when serving it to my boys so I make sure I get them out for them if I can, but if you are serving it to guests I'd just give them a heads up.