Core and seed the peppers. Cut them lengthwise into ¼-inch-thick strips.
Cut the tomatoes in half.
In a medium-size heavy saucepan over low heat, combine the peppers, tomatoes, lemon juice, ginger, anise, pepper, and sugar. Cover, and simmer, stirring occasionally, for 50 minutes.
Transfer the soup, in batches, to a food processor and purée.