Heat 1 tablespoon oil in 12-inch skillet over medium-high heat until shimmering. Brown half of eggplant lightly on all sides, 5 to 7 minutes; transfer to slow cooker. Repeat with 1 tablespoon more oil and remaining eggplant.
Transfer to slow cooker. Working in two batches, repeat sauté with 2 tablespoons more oil and zucchini; transfer each batch to slow cooker.
Heat remaining 2 tablespoons oil in skillet over medium-high heat until shimmering. Add onions, bell peppers, garlic, and thyme and cook until vegetables are softened and lightly browned, 8 to 10 minutes. Stir in flour and cook for 1 minute. Slowly whisk in reserved tomato juice, scraping up any browned bits and smoothing out any lumps; transfer to slow cooker.
Stir tomatoes into slow cooker. Cover and cook until vegetables are tender, 4 to 6 hours on low. Stir in basil, season with salt and pepper to taste, and serve with Parmesan. (This dish does not hold well on warm setting.).