Thinly slice daikon radish, carrot and lettuce leaves and soak them in a bowl of cold water. Wash and dry mini tomatoes. You can serve as much or as little salad as you like so I didn't include measurements for this part.
Mix 2 tbsp Japanese mayonnaise, 1 tsp Japanese soy sauce (koikuchi shoyu) and ⅛ tsp Japanese mustard (karashi) in a small bowl until combined, set aside for later.
Patty
Take a large mixing bowl and add 200 g ground pork, 50 g ground beef, ½ onion (grated), 1 egg, 4 tbsp panko breadcrumbs, 2 tbsp plain yogurt, 2 tbsp mayonnaise, ½ tbsp yellow miso paste (awase), ¼ tsp salt, ¼ tsp sugar, 1 pinch nutmeg powder, and 1 pinch ground black pepper.
Knead everything together until well distributed and you have a uniform sticky mixture.
Divide the mixture into equal portions. Lightly oil your hands to stop sticking, and throw each patty between your hands about 10 times to remove excess air. Shape into an oval and make a dent in the center. Place each patty on a square of baking paper to make it easy to transfer to the pan later. You can neaten the shape once it's on the baking paper.
Heat a pan on medium and add a small amount of oil. Flip the patties into the pan with the baking paper side facing up and carefully peel it off. Fry for 2 minutes on each side, or until they have a nice golden-brown crust all over.
Reduce the heat to low, add a few teaspoons of warm water to the pan and cover with a lid. Steam-fry for 6 minutes or until cooked through.
Remove the lid and top each patty with cheddar cheese (optional). If you want it to look more like Bikkuri Donkey's, you can cut cheese slices into strips and make a cross shape on top. Place a lid on top and steam until melted, then transfer to a warm plate.
Sauce
In the same pan, add 2 tbsp onion (finely diced) and fry them in the leftover fat from the patties until softened. Wipe out excess oil if needed.
Once the onions are soft and golden, add 2 tbsp orange juice, 1 tbsp Japanese soy sauce (koikuchi shoyu), 1 tbsp sake, 1 tbsp mirin and ¼ tsp dashi granules. Mix it well and let it boil for 30 seconds.
Serving
Drain the salad and squeeze to remove the excess water. Place it on the plate and top it with the seasoned mayonnaise and a mini tomato. Arrange a portion of rice and the hamburg next to it, then drizzle the hamburg with the sauce from the pan. Enjoy!
Notes
Shape and cook without a pause: This meat is kept loose on purpose. Carry a shaped patty in your hands or leave it sitting, and it slumps or cracks.Leave the looseness alone: Even fully kneaded, it stays softer than an everyday hamburger steak. Avoid firming it up with extra dry breadcrumbs, doing so loses the softness that lets chopsticks cut right through it.Keep the patties thin: The restaurant's patty is a low, thin oval.Cook the pork-heavy patty through: Clear juice from the center is your signal that it is done.Keep the sauce boil to 30 seconds: Past that, you taste the salt of the soy sauce before the sweetness of the onion.Go easy on the sauce: The restaurant pours a thin sauce, and only a little of it. Spoon it onto the patty alone and leave the rice white.