Preheat grill to medium-low. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 7 seconds.) Brush eggplant wedges on all sides with 2/3 cup oil, and season with 1 teaspoon salt.
Place eggplant on grill rack in a single layer. Cover grill, and cook, turning occasionally, until softened and lightly charred, about 8 minutes total.
Meanwhile, whisk together molasses, lemon juice, garlic, mint, remaining 2 teaspoons salt, the pepper, and remaining 2/3 cup oil. Add warm eggplant, and toss.
This recipe calls for pomegranate molasses. You can buy this ingredient from Kalustyan's, 800-352-3451.