In a small bowl combine the yogurt and fennel seed. Cover and let stand at room temperature for 30 minutes.
Meanwhile, in a large saucepan cook and stir the sweet peppers, shallots, and cardamom in the hot oil about 15 minutes or until peppers are just beginning to soften. Add chicken broth, water, and vinegar. Bring to boiling; reduce heat. Simmer, covered, for 5 minutes more.
Remove from heat and let cool slightly. In a blender container or food processor bowl, blend or process the mixture, half at a time, until smooth. Return all soup to saucepan. Cook and stir over medium heat until heated through.
To serve, ladle blended soup into individual bowls. Top with a dollop of yogurt mixture, some of the cucumber, and black pepper. Can be served warm or chilled. Makes 4 servings.