Combine all patty ingredients (pork, beef, grated onion, egg, panko, yogurt, mayo, miso, salt, sugar, nutmeg, pepper) in a bowl.
Knead until well distributed and the mixture is uniform and sticky.
Shape into equal patties with lightly oiled hands, optionally pressing cheddar on top.
Heat oil in a skillet over medium-high and brown the patties on both sides.
Add a splash of hot water, reduce heat to low, cover and steam 5-8 minutes until cooked through (juices run clear when pressed). Remove patties.
Onion sauce: add the finely diced onion to the same pan, then the orange juice, soy sauce, sake, mirin and dashi granules. Simmer until combined and slightly thickened, then spoon over the patties.
Salad dressing (optional): whisk the mayo, soy sauce and mustard; toss with the shredded vegetables.