Heat the oil in a heavy medium saucepan over medium-high heat. Add the shallots and sauté for 5 minutes. Add the red peppers with their liquid. Stir in the sugar; sauté 2 minutes. Add 2 cups of broth and simmer for 5 minutes. Remove from heat and let the soup cool slightly.
Working in batches, puree the soup in a blender. Return the soup to the pan. Bring to a simmer; stir in the orange juice. Thin the soup with additional broth, if desired. Season with salt and pepper.
PREPARE THE GARNISH:
In a small bowl, whisk the whipping cream and orange zest until slightly thickened. Season with salt and pepper. Ladle the soup into bowls. Drizzle the orange cream over the soup. Sprinkle with basil and serve. Alternately, you can choose to garnish individual servings, as desired.