Step 1Heat the oven to 400 degrees. Halve the tomatoes lengthwise and place on a foil-lined rimmed baking sheet. Drizzle the olive oil over the tomatoes, and sprinkle over one-half teaspoon salt and one-fourth teaspoon pepper. Roast the tomatoes for 20 minutes to soften. Remove from the oven and set aside.
Step 2While the tomatoes are roasting, steam the cauliflower in a steamer set over a pot of boiling water. Steam the cauliflower until tender, then remove from heat and set aside.
Step 3Roast the peppers: Place the peppers on a rack set over a gas stove-top burner heated over high heat. Roast until the skin on all sides is charred, turning frequently. Place the peppers in a bowl and cover with plastic wrap and set aside until the peppers are cool enough to handle. Peel the charred skin from the peppers, then stem and seed the peppers. Mince the peppers. You should have about 2 cups (1 pound) minced roasted pepper.
Step 4Combine the roasted tomatoes (with any juices), cauliflower, minced peppers, garlic, lemon juice, tomato juice, tomato paste, basil leaves and vegetable broth in a pot or large bowl. Puree the mixture using an immersion blender, or in batches using a blender, before pushing through a strainer into a heavy-bottom soup pot.
Step 5Bring the soup to a simmer over medium heat, stirring frequently. Stir in the cream and continue to heat until hot. Season to taste with salt and pepper, and stir in sugar to sweeten as desired.