Preheat the oven to 450 degrees F (230 degrees C).
Place tomatoes and onion on a rimmed baking sheet; drizzle with about 1/4 cup olive oil. Season with salt and pepper.
Roast in the preheated oven until well browned and softened, about 15 minutes. Let cool until ready to use.
Heat remaining olive oil and tomato juice in a saucepan over medium-low heat. Add garlic and the roasted onion; cook until softened, about 10 minutes.
Chop the roasted tomatoes and add to the soup. Add bell peppers, banana peppers, chicken broth, sugar, and butter. Simmer until vegetables are very tender, about 20 minutes. Remove from heat and puree until smooth in a blender or using an immersion blender.
Return bisque to the pan and add cream. Simmer over low heat until heated through, about 15 minutes. Garnish with basil.