Preheat oven to 400 degrees. Arrange tomatoes, eggplant, carrots, onion and garlic cloves in a single layer on two baking sheets. Drizzle olive oil evenly over vegetables; sprinkle with pepper and ¼ teaspoon salt. Roast in preheated oven until tender and lightly browned, about 40 minutes, rotating baking sheets halfway through.
Reserving a couple slices of eggplant for garnish, scrape the rest of the vegetables and cooking juices into a large Dutch oven. Stir in vegetable broth and coconut cream. Bring to a boil over medium-high. Remove from heat. Purée soup with an immersion blender or transfer to a blender and pulse. Stir in vinegar and season with salt and pepper, to taste. Divide between two bowls, top with eggplant pieces and torn basil.