Preheat broiler to high. Arrange bell peppers skin side up on baking sheet. Broil, watching carefully, until skins are blackened, about 10 minutes. Remove peppers from oven and let cool. Peel over a bowl to collect juices; set peppers and juices aside.
In a large pot over medium-high heat, warm olive oil. Add shallots, salt, and cayenne and cook, stirring until soft, 3 minutes. Add broth and cauliflower. Bring to a boil, then lower heat to a simmer. Cover and cook 20 minutes. Add peppers with juices and cook, covered, until cauliflower is tender, 10 minutes. Purée in batches in a blender and add sugar. Add pepper to taste.
Serve hot or cold, garnished with a drizzle of extra-virgin olive oil, some chives, and a squeeze of lemon juice if you like.
Note: Nutritional analysis is per serving.