Prep: 25 minutes; Cook: 15 minutes; Total Time: 40 minutes.
Preheat broiler. In batches, place eggplant, bell peppers, and zucchini on 2 baking sheets lightly coated with cooking spray. Sprinkle with salt and black pepper. Broil for 3–4 minutes per side or until golden. Transfer to plate; set aside.
Bring chicken broth and water to a boil in a pan; slowly whisk in polenta. Simmer for 5 minutes or until thickened. Stir in goat cheese and 3 tablespoons Parmesan cheese.
Spoon polenta into 4 bowls; top evenly with vegetables (1 cup each), basil, and remaining 1 tablespoon Parmesan.