Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.
Place eggplant, zucchinis, tomatoes, onion, bell pepper, and garlic in a single layer on the prepared baking sheet. Drizzle with olive oil, rosemary, salt, and pepper; toss vegetables until well coated.
Roast in the preheated oven until slightly tender; about 20 minutes. Mix and roast for another 12 minutes. Reduce heat to 300 degrees F (150 degrees C) and cook until vegetables begin to caramelize; about 10 minutes. Drizzle with balsamic vinegar.