Preheat the oven to 425°F. Place the eggplant, zucchini, bell peppers, cherry tomatoes, and red onion on a large rimmed sheet pan. Add the minced garlic, olive oil, thyme, salt, and pepper. Toss everything until the vegetables are evenly coated, then spread them into a single layer.
Roast the vegetables for 25 to 30 minutes, stirring once halfway through, until they are tender and lightly browned at the edges.
While the vegetables roast, bring the vegetable broth to a boil in a medium saucepan. Slowly whisk in the polenta. Reduce the heat to low and cook, stirring often, for 15 to 20 minutes until the polenta thickens.
Remove the polenta from the heat. Stir in the milk, Parmesan cheese, and butter until the mixture is smooth and creamy.
Spoon the creamy polenta into bowls and top with the roasted vegetables. Finish with a few fresh basil leaves.