Step 1

Preheat oven to 475°F with racks in upper third and lower third positions. Cut eggplant in half lengthwise. Reserve 1 of the eggplant halves for another use. Cut remaining eggplant half in half lengthwise; then slice crosswise into ½-inch-thick pieces. Place in a medium bowl. Add bell pepper strips, oil, and ¼ teaspoon each of the salt and black pepper to eggplant; toss to coat. Spread mixture in an even layer on an 18- x 13-inch rimmed baking sheet; set aside.

Step 2

Stir together lemon zest, 2 teaspoons of the rosemary, ¼ teaspoon of the salt, and remaining ¼ teaspoon black pepper in a small bowl. Using your hands, rub about ½ teaspoon lemon mixture under skin of each chicken thigh. Sprinkle chicken skin evenly with ½ teaspoon of the salt. Place 1 chicken thigh, skin side up, in each corner of baking sheet with eggplant mixture. Bake on lower rack in preheated oven 15 minutes.

Step 3

Remove baking sheet from oven. Increase oven temperature to broil. Stir zucchini, tomatoes, and ¼ teaspoon of the salt into eggplant mixture on baking sheet; spread in an even layer (do not move chicken). Immediately return to lower oven rack; broil just until zucchini is tender-crisp, about 10 minutes. Transfer baking sheet to upper rack, and broil until chicken skin is crisp and zucchini mixture is charred in spots, about 3 minutes. Sprinkle zucchini mixture with parsley and remaining 1 teaspoon rosemary and ¾ teaspoon salt. Drizzle with balsamic glaze, and stir to combine. Garnish with additional parsley, and serve.