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.
Heat a pan on medium and add a small amount of oil. Place the patties in the pan with the dent-side facing up and fry for 2 minutes on each side to create a nice crust.
Once both sides are browned, reduce the heat to low, add a few teaspoons of warm water to the pan and cover with a lid. Steam 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
Reusing the same pan, add 2 tbsp onion (finely diced) and fry them in the leftover fat from the patties until soft
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!