1 1/2 pounds fresh shiitake mushrooms (2 to 3 in. wide) or Asian eggplant, or a combination of both

Rinse 1 1/2 pounds fresh shiitake mushrooms (2 to 3 in. wide) or Asian eggplant, or a combination of both. Remove tough stems from shiitakes. Slice eggplant in half crosswise; cut each piece in half lengthwise. If using eggplant, place a rack over about 1 inch water in a 6- to 8-quart pan. Pile eggplant on rack, bring water to a boil over high heat, cover, and steam eggplant until soft, about 5 minutes. Let stand until cool enough to handle. Thread two or three mushrooms (horizontally through cap) or one piece eggplant onto each soaked 12-inch wood skewer. Brush vegetables lightly with Asian sesame oil or vegetable oil. Place on a lightly oiled grill over a solid bed of medium-hot coals or medium heat on a gas grill (you can hold your hand at grill level only 3 to 4 seconds); close lid on gas grill. Cook, turning once, until tender when pierced, 6 to 8 minutes. Serve with ginger or ponzu dipping sauce.