Preheat oven to 400°.
To prepare salad, bring 4 cups water to a boil in a large saucepan. Add barley. Cover, reduce heat, and simmer 45 minutes or until tender. Let stand, covered, 5 minutes. Spoon barley into large bowl.
Place peppers and eggplant on one jelly-roll pan coated with cooking spray; place zucchini and squash in another jelly-roll pan coated with cooking spray. Coat vegetables with cooking spray; sprinkle with 1/4 teaspoon salt and black pepper. Place pan with squash on top rack in the oven and pan with eggplant on middle rack. Bake at 400° for 12 minutes or until squash and zucchini are tender. Remove pan with squash, and move pan with eggplant to top rack. Bake peppers and eggplant an additional 8 minutes or until tender. Cool. Cut vegetables into 1/2-inch pieces. Add vegetables, parsley, and next 4 ingredients (through garlic) to barley; toss gently.
To prepare dressing, combine vinegar, oil, and 1/2 teaspoon salt, stirring well with a whisk. Add dressing to barley mixture; toss. Sprinkle with cheese.