Using a vegetable peeler, carefully peel long strips of cucumber. When you get too close to the seeds, turn the cucumber, and continue until all you have left are the seeds. Place the cucumber strips in a bowl with ¼ cup rice vinegar and let sit at room temperature while you prepare the rest of the meal. Add the chili slices to the rest of the vinegar and let sit at room temperature.
Slice the eggplant into ½ - ¾ inch slices.
Combine the batter mix from the kit with 10 tablespoons water and whisk until smooth. Put the panko breadcrumbs from the kit in a shallow bowl or on a plate. Heat the Katsu sauce from the kit in a small saucepan and keep warm. Coat the eggplant in batter and dredge in panko crumbs.
Add enough oil in a large skillet to come up ¼ inch. Heat over medium-high heat until it begins to shimmer. Fry the eggplant slices in batches (do not overcrowd the pan) for 3-5 minutes per side or until golden brown and the eggplant is tender. Continue with the rest of the eggplant.
Serve the eggplant over rice drizzled with the warm Katsu sauce. Garnish with green onion slices and quick pickled chilies and serve with the cucumber salad.