1) Prepare a medium fire in a charcoal griddle with a cover, or preheat a gas griddle to medium.
2) Mix the mirin, sake and soy sauce in a small, heavy fire-proof saucepan. Place the pan on the griddle rack, bring the mixture to a simmer and cook until reduced to a slightly thicker consistency, 15-20 minutes. Set the glaze aside (it will thicken slightly as it cools).
3) To make the mayonnaise, mix all of the ingredients in a small bowl. Cover and refrigerate until serving.
4) Mix the sesame dressing and ponzu sauce in a small bowl. Place the spinach in a large bowl and toss lightly with the dressing. Cover and refrigerate until serving.
5) To make the patties, mix the mirin, sake and soy sauce in a small bowl. Stir in the miso and blend evenly. Spread the beef out in a large, shallow pan. Distribute the miso mixture over the meat and sprinkle evenly with the spring onion, ginger, garlic, pepper and salt. Handling the meat as little as possible to avoid compacting it, mix well.
6) Divide the mixture into six equal portions and, with cupped hands, toss one portion of the meat back and forth from hand to hand to form a loose ball. Pat the meat portion lightly on a flat surface to form a patty to fit the buns. Press the centre of the patty down with your fingertips to create a slight indention in the middle of the patty. Repeat with the remaining meat portions.
7) When the griddle is ready, brush the rack with vegetable oil. Place the patties on the rack and baste each patty with the glaze. Cover and cook until browned on the bottom, 3-4 minutes, basting each patty again with the glaze. Turn the patties and brush the cooked side with the glaze. Cook, brushing frequently with the glaze, until done to preference, 4-5 minutes longer for medium.
8) During the last few minutes of cooking, place the baps, cut side down, on the outer edges of the rack to toast lightly.
To assemble the burgers, place an equal portion of the spinach on each bap bottom and top with a patty. Spread the mayonnaise over the cut sides of the bap tops. Add the bap tops and serve.