Preheat oven to 400°F (200°C). Toss eggplant, zucchini, and bell pepper with 2 tbsp olive oil, salt, and pepper on a sheet pan.
Roast 25-30 minutes, stirring once, until tender and lightly browned at the edges.
Meanwhile, heat remaining 2 tbsp olive oil in a large pot over medium heat. Add onion and cook 5 minutes until softened, then stir in garlic and cook 1 minute.
Add tomatoes and thyme to the pot and simmer 15-20 minutes, stirring occasionally, until slightly thickened.
Fold the roasted vegetables into the tomato sauce along with fresh basil. Simmer 5 more minutes to meld the flavors. Season with salt and pepper.
While the ratatouille finishes, bring vegetable broth to a boil in a separate pot. Whisk in polenta in a steady stream, then reduce heat to low and cook, stirring frequently, 20-25 minutes until thick and creamy. Stir in chives, salt, and pepper.
Spoon ratatouille over a bed of soft polenta and garnish with fresh basil.
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