Roast eggplant and zucchini: Put oven racks in upper and lower thirds of oven and preheat oven to 425°F.

Toss eggplant and zucchini with 5 tablespoons oil, ¾ teaspoon salt, and ¾ teaspoon pepper in a bowl, then spread in 2 oiled large shallow (1-inch-deep) baking pans. Roast vegetables in oven, stirring occasionally and switching position of pans halfway through baking, until vegetables are golden brown and tender, 20 to 25 minutes total. Combine vegetables in 1 pan and cool, reserving other pan for cooling barley.

Cook barley: Heat 2 tablespoons oil in a 3- to 4-quart heavy pot over moderately high heat until hot but not smoking, then cook scallion, cumin, coriander, and cayenne, stirring, until fragrant, about 1 minute. Add barley and cook, stirring until well coated with oil, 2 minutes more. Add broth and water and bring to a boil. Reduce heat and simmer, covered, until all of liquid is absorbed and barley is tender, 30 to 40 minutes. Remove from heat and let stand, covered, 5 minutes. Transfer to reserved shallow baking pan and spread to quickly cool, uncovered, to room temperature, about 20 minutes.

Make dressing and assemble salad: Whisk together lemon juice, garlic, sugar, and remaining ¼ teaspoon salt, ¼ teaspoon pepper, and 3 tablespoons oil in a large bowl. Add barley, roasted vegetables, and remaining ingredients to bowl with dressing and toss until combined well. Serve with cheese slices.

Do ahead: Salad can be made 1 day ahead and chilled, covered. Return to room temperature before serving.