Wash and dry all vegetables except for onions. Cut potatoes into 1-inch thick lengthwise wedges. Steam wedges on a rack over boiling water (covered) for 10 minutes to pre-cook potatoes. Remove potatoes from steam and pat dry with paper towels.

Prepare remaining vegetables: cut eggplant lengthwise into 1-inch thick slices; cut zucchini and yellow squash in half lengthwise; seed and quarter green and red peppers. Place potatoes and all other vegetables on baking sheets and brush with olive oil to prevent sticking during grilling. Prepare grill.

When grill is ready, lightly oil the grill tray. Place eggplant, squash and mushrooms on the grill crosswise so they don't fall through the grill tray. Place the tomatoes and the peppers in a wire grilling basket or on a grilling tray suitable for small foods so they don't fall through into the grill. Place onions and potatoes directly on grill.

With the grill lid closed, grill all vegetables for 5 minutes. With tongs and a metal spatula, turn the vegetables and grill the other side, with the lid closed, for another 5-6 minutes. If all vegetables don't fit on the grill, cook in batches.

When vegetables are cooked, arrange on a large serving platter (slice portobello mushrooms if they're large). Sprinkle vegetables with the fresh thyme leaves or chives, if desired. Serve salad warm or at "picnic" temperature no need to chill.