Make a criss-cross pattern on the cut sides of the aubergines and place them, cut side down, on a grill pan. Cook for 7–10 minutes under a preheated hot grill until charred. Mix together the miso paste, 2 tablespoons vinegar, the sugar and sake or water. Turn the aubergines over and brush with the miso mixture. Return to the grill for 3–5 minutes until the aubergine is soft, then sprinkle with the sesame seeds and cook for 1 minute more.
Meanwhile, cook the soy beans in a saucepan of lightly salted boiling water for 2 minutes until soft. Drain and cool under cold running water. Toss the beans together with the noodles, cucumber, spring onions, the remaining vinegar and season with salt. Serve with the grilled aubergine.