Cut each eggplant in half lengthwise. Score the cut side with shallow diagonal cuts about 2–3mm apart, then cut crosswise into 2 wedges per half. Soak in cold water for a few minutes, drain, and pat dry. Cut peppers in half lengthwise, deseed, then cut each half diagonally.
In a bowl or container, combine mentsuyu, water, and grated ginger. Stir to combine.
Heat sesame oil in a frying pan over medium heat. Cook the eggplant skin-side down for 2–3 minutes. Add the pepper, flip the eggplant, and continue cooking until both are golden and tender — another 2–3 minutes per side.
Transfer the hot vegetables directly into the tsuyu. Press plastic wrap against the surface and let sit for at least 15 minutes at room temperature, or refrigerate for 1–3 hours for deeper flavour.
Shred shiso and sliver myoga. Serve the chilled vegetables in a bowl with plenty of the tsuyu, generously topped with bonito flakes, shiso, and myoga.
