Soak the panko in the milk for a few minutes. This paste (a panade) is what keeps lean beef juicy.
Mix the beef, half the diced onion, the soaked panko, egg, salt, pepper, and nutmeg. Knead with your hand for a full minute until the mixture turns slightly sticky and pale. This is the opposite of American burger advice, and it is correct here; the kneading gives hambagu its bouncy, tender texture.
Divide into 4 oval patties about 2cm thick. Toss each one between your palms a few times to slap out air pockets, then press a shallow dimple into the center so they cook flat.
Heat the oil in a lidded pan over medium-high. Brown the patties 2 minutes per side.
Add 3 tablespoons of water, cover, drop the heat to medium-low, and steam 5 to 6 minutes until the centers hit 70C (160F). Move the patties to a plate.
Add the remaining onion to the pan and cook 2 minutes in the leftover fat. Stir in the ketchup, Worcestershire, soy sauce, rice vinegar, and water. Simmer 2 minutes until it coats a spoon, then return the patties and turn them in the sauce.
Serve with rice and something green, sauce spooned over the top.