Dice the onion into small pieces.
Grab a large pan or skillet and heat up the cooking oil. Saute the onions until they are translucent.
Move the onions to a separate bowl and let them cool completely.
In a bowl, combine the beef and pork with salt and black pepper.
Add in 1 egg, panko, and milk. Use a silicone spatula to mix the ingredients.
Once combined, continue to mix and knead the meat with your hands until it's quite sticky.
Divide into 4 parts and shape your patties. You want to mix them well until they have a smooth texture.
Toss each patty from one hand to the other and press them to remove any air bubbles that have formed.
Shape your oval patties and cover them with plastic wrap. Let them cool in the fridge for about half an hour.
To cook the patties, heat up the oil and start frying your patties. While still cool, make a dent in the middle of each patty. This helps the patties keep their texture.
Cook each patty for about 3 minutes or so on each side on high heat or medium-high heat. Cook for 5 minutes if you like them very well done.
Once patties are browned remove them and set them aside.
In the same oil, fry 2 eggs and then cut them in two. Set aside.
Leave the fatty oil and grease in the pan and add the butter, wine, ketchup, and tonkatsu sauce.
Mix all of the sauce ingredients and bring them to a simmer on medium low heat. Cook for a couple of minutes or so until the alcohol evaporates and the sauce thickens.
Once thickened drizzle all over your patties. Place half an egg on each patty and enjoy.