In a large bowl, toss green beans with the ⅓ cup balsamic vinegar.
Grill the eggplant slices (on a grill or grill pan) 8 to 10 minutes, turning frequently.
In a large salad bowl, toss together bell peppers, greens, onions, olive oil, lemon juice 2 tablespoons balsamic vinegar. Add salt and pepper to taste.
Drain the green beans and then arrange grilled eggplant and green beans on top of the salad. Serve immediately.