To prepare dressing, combine first 9 ingredients in a bowl; stir with a whisk.
To prepare salad, combine 3 tablespoons dressing and eggplant, tossing to coat. Arrange eggplant slices in a single layer on a baking sheet coated with cooking spray. Broil 4 minutes on each side. Combine remaining dressing, eggplant, jicama, and bell peppers, tossing to coat.