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Heat grill to medium-high (about 450°F)
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Slice zucchini, summer squash, and onion into 1/4-inch thick strips or slices.
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Seed and cut bell peppers into 1-inch wide strips.
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Place vegetables in a large casserole dish. Drizzle with olive oil and sprinkle with salt and pepper. Toss to coat vegetables with oil (be careful not to separate onion rings).
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Place vegetables on grill in a single layer. Close lid and grill for about 3 to 5 minutes, until bottom side has grill marks.
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Turn vegetables over. Close lid and grill for another 3 to 5 minutes, until bottom side has grill marks and vegetables have softened. Place grilled vegetables in a bowl or casserole dish and cover with foil to keep warm.
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Slice rolls in half horizontally. Place cut side down on grill. Remove bread from grill when toasted, about 2 minutes. Watch closely so bread does not burn.
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Spread soft cheese on toasted rolls. Stack vegetables on bottom half of rolls. Drizzle balsamic glaze on vegetables. Cover with top half of rolls.