In a small saucepan, combine couscous, 1 cup water, and 1/2 teaspoon salt. Bring to a boil, stir once, and reduce to a simmer. Cover and cook until couscous is tender, about 15 minutes.
Meanwhile, in a large skillet with a tight-fitting lid, heat oil over medium-high. Add eggplant and shallots and stir to coat; season with salt and pepper. Cover and cook, stirring frequently, until shallots are caramelized and eggplant is cooked through, 10 to 12 minutes.
In a serving bowl, combine eggplant mixture and couscous. Stir in vinegar and basil and season salad with salt and pepper.