Preheat the oven to 450 degrees . Add the eggplant, zucchini, tomatoes, onion, chile pepper, bell pepper, garlic, thyme and rosemary to a rimmed baking sheet as you chop them. Drizzle with enough EVOO to coat (about 1/4 cup); season liberally with salt and pepper. Roast until just tender, 18 to 22 minutes.
Meanwhile, in a large saucepan, heat the milk and chicken (or vegetable) stock. Whisk in the polenta and cook, stirring, until creamy and thick, 2 to 3 minutes. Turn off the heat and stir in the cheese, honey and butter; season with salt and pepper.
Serve the ratatouille on a bed of the polenta and top with the basil.