1. Stir together balsamic vinegar and next 3 ingredients in a small bowl. Slowly whisk oil into marinade until blended.
2. Combine eggplant and next 3 ingredients in a large bowl. Pour marinade over vegetables, tossing to coat. Let stand, stirring occasionally, 1 hour.
3. Secure vegetable pieces onto 12 to 15 skewers, alternating eggplant, zucchini, peppers, and mushrooms.
4. Grill over medium-high heat about 5 minutes per side or until eggplant becomes tender and slightly browned. Arrange on a serving platter, and sprinkle evenly with basil and pepper.