Heat gas grill on medium or charcoal grill until coals are ash white.
Combine all aioli spread ingredients in bowl; mix well. Set aside.
Place butter into another bowl; microwave 30 seconds or until melted. Stir in cumin, rosemary, coriander, oregano and salt.
Place vegetables onto grill. Grill, turning vegetables occasionally and brushing with butter mixture, 6-12 minutes or until vegetables are tender. Remove onion and zucchini to plate.
Turn portabella mushrooms round-side up. Top each mushroom with 1 slice cheese; continue grilling 2-3 minutes or until cheese is melted.
Spread about 1 tablespoon aioli onto 1 side of each toasted bread slice. Layer 4 slices bread with grilled zucchini, onion slices and mushrooms. Top with second slice of bread. Serve warm.
– To clean mushrooms, wipe with paper towel. Use spoon to scoop out gills under cap of each mushroom; discard gills.
– If mushrooms are too large, trim to fit bread.