Miso Barbequed Tofu

• 12 japanese eggplants
• 8 shiitake mushrooms (whole)
• 4 atsu age cakes
• 1/2 mirin
• 1/4 barley miso
• 120 ml water
• 60 ml sauce (plum)
• 14 gr brown sugar
• 8 gr arrowroot powder
• some green onions in a saucepan