Cook the onions: Finely chop 1/2 medium onion and sauté in a pan with a little oil until soft. Remove from the heat and allow to cool.
Prepare the burger patties: Next, in a large bowl soak 4 tbsp panko in 2 – 3 tbsp of milk, add the minced meat and mix together by hand. Then add the cooled cooked onions, 1 egg, 1/2 tbsp worcestershire sauce and 1/2 tbsp soy sauce, as well as salt and pepper to taste. Mix well once more.
Mould the mixture into patties: Separate the mixture into 4 equally sized portions and mould into rounded patties, indenting the centre a little with your finger to ensure it cooks through evenly. Dust each patty with plain flour and dip into 1 beaten egg.
Cover the patties with panko breadcrumbs: Spread the panko breadcrumbs on a plate and cover the patties on both sides with the breadcrumbs. Fill a wok with oil for deep frying. Heat the oil until a small sprinkle of panko sizzles when added.
Cook the burger patties: Deep fry the burger patties in cooking oil on a medium-high temperature (about 150°C/300°F) turning several times until golden brown on the outside. Remove from the oil and drain on a wire rack.
Prepare a brioche bun: To serve, make a Menchi Katsu Burger by slicing and buttering a brioche bun, adding a handful of shredded white cabbage, a menchikatsu burger and drizzling with tonkatsu sauce. Alternatively make a Menchi Katsu Sandwich with white bread and cabbage, or simply serve on a plate with rice, shredded cabbage and tonkatsu dipping sauce.