Char peppers over gas flame or in broiler until blackened on all sides. Enclose in paper bag and let stand 10 minutes. Peel, seed and slice peppers. Heat oil in heavy large saucepan over medium heat. Add shallots, garlic and thyme and sauté 3 minutes. Add 3 cups broth and all but 4 slices of roasted pepper. Simmer uncovered until peppers are very soft, about 20 minutes.
Working in batches, purée soup in blender until smooth. Return to same pot. Add half and half, vinegar and cayenne pepper. Rewarm soup, thinning with additional broth, if desired. Season to taste with salt and pepper. Ladle soup into bowls. Garnish with reserved pepper strips and basil.