1) Cut eggplant and peppers. In a bowl, mix together 1/4 cup mirin and 2 Tbsp each tamari (or soy sauce) and oil; toss the eggplant and pepper slices in this mixture and let marinate while you prepare the noodles.
2) Stir together water, cornstarch, chili paste, and the remaining 6 tbsp each of mirin and tamari in a bowl.
3) Prepare soba noodles as directed by package.
5) Heat the remaining tablespoon of oil in a 1 - 2 quart heavy saucepan over moderate heat until hot but not smoking. Add ginger and the white part of the scallions and cook, stirring, until fragrant, about 30 seconds. Add cornstarch mixture and simmer, stirring occasionally, until slightly thickened, about 2 minutes. Remove from heat and cover to keep warm.
6) Preheat broiler. Line two large baking pans with foil and lightly oil the foil. Arrange the eggplant slices on the baking sheets. Broil (four inches under the broiler), rotating the pan as needed, until the eggplant is browned, about 5 minutes (watch carefully, it burns easily). Flip eggplant to other side and broil until brown and tender, about 3 to 5 minutes. Set aside and broil the other peppers and zucchini in the same manner, but stand guard while they cook. These vegetables will take just a few minutes and burn quickly.
7) Cut the eggplant crosswise into 1/2 inch wide pieces. Toss the noodles with the vegetables, sauce, and remaining scallions. Season to taste with salt and pepper.