Sauté the onion in a pan with a little oil until translucent and softened. Let it cool completely.
In a large bowl, combine ground beef, ground pork, cooled sautéed onion, panko breadcrumbs, milk, egg, salt, black pepper, and nutmeg. Mix well until everything is evenly incorporated and slightly sticky.
Divide the mixture into 4 equal portions and shape each into an oval patty, about 1.5 cm thick. Make a shallow indentation in the center of each patty to prevent it from bulging during cooking.
Heat vegetable oil in a large frying pan over medium heat. Place the patties in the pan and sear for about 3-4 minutes on one side until golden brown.
Flip the patties, reduce heat to low, cover the pan, and cook for another 8-10 minutes, or until cooked through. Remove the patties from the pan and set aside.
In the same pan (without washing), add soy sauce, mirin, sake, and sugar. Bring to a simmer, scraping up any browned bits from the bottom of the pan. Cook for 1-2 minutes until the sauce slightly thickens.
Return the hamburger steaks to the pan, spoon the sauce over them, and gently heat for about 1 minute.
To serve, place a hamburger steak on a plate, top with a generous amount of grated daikon radish, and garnish with chopped green onions.
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