Blend chickpeas, tahini, lemon juice, cold water, garlic, 1/8 teaspoon salt and 1 teaspoon olive oil in a small food processor until thick and smooth, scraping the sides as needed. Refrigerate while cooking vegetables.
Heat a grill pan over medium-high heat. Brush eggplant and zucchini with remaining oil and season with remaining salt and pepper.
Grill vegetables in 2 batches for 3 to 5 minutes per side until browned and fully tender, giving eggplant additional time if its center is still firm. Transfer to a shallow container and refrigerate promptly for about 40 minutes until cold.
Spread hummus over the cut faces of both rolls. Layer chilled eggplant and zucchini over the bottoms and add shredded dry cabbage.
Close with the roll tops and cut in half. Serve cold or refrigerate at 40°F or below, transporting with ice packs; prep time includes vegetable chilling.