If Using a Grill (recommended): Preheat a gas or charcoal grill to medium heat and place eggplants directly over heat source. Cook, turning occasionally with tongs, until eggplants are completely tender and well charred on all sides, 30 to 40 minutes. Wrap with foil and let rest 15 minutes. Continue to step 3.
If Using the Broiler: Adjust rack to 6 inches below broiler element and preheat broiler to high. Place eggplants on a foil-lined rimmed baking sheet and prick all over with a fork. Broil, turning occasionally, until charred on all sides and completely tender, about 30 minutes (timing may vary depending on broiler strength). Eggplants should be very, very tender when cooked; if eggplant is not fully tender once skin is charred all over, switch oven to 425°F and roast until fully tender (a toothpick or skewer inserted near stem and bottom ends should not meet any resistance). Remove from oven and gather up foil, crimping it around eggplants to form a sealed package. Let eggplants rest for 15 minutes. Continue to step 3.
