Heat the barbecue to high heat. Place the eggplant on a baking sheet, brush with oil and season. Grill for about 15 minutes, turning and brushing with more oil halfway through, until they are golden and tender.
In the meantime, put the couscous in a large bowl, pour the broth over it, then cover and let it rest for 10 minutes. Mix the tomatoes, mint, goat cheese, and remaining oil. Fluff the couscous with a fork, then combine the eggplant, tomato mixture, and lemon juice.