Process chickpeas, tahini, lemon juice, cold water, garlic, 1/8 teaspoon salt, and 1 teaspoon oil until thick and smooth, scraping sides as needed. Refrigerate while cooking vegetables.
Heat grill pan over medium-high. Brush eggplant and zucchini with remaining oil; season with remaining salt and pepper.
Grill in 2 batches, 3 to 5 minutes per side, until browned and fully tender; cook eggplant longer if centers remain firm. Transfer to a shallow container; promptly refrigerate about 40 minutes until cold.
Spread hummus on cut faces of both rolls. Layer bottoms with cold eggplant, zucchini, and dry cabbage.
Close and halve. Serve cold or refrigerate at 40°F or below; transport with ice packs. Prep time includes chilling.