Preheat oven to 400F. Remove giblets from game hens. Pat dry. Tie legs together to hold shape. Place game hens in a large roasting pan. Combine broth, vinegar, honey, oil, cumin, aniseed and cinnamon in heavy medium saucepan. Simmer until mixture thickens slightly, stirring constantly, about 5 minutes. Remove glaze from heat. Brush glaze over hens. Sprinkle generously with salt and pepper. Roast until last drops of juices run clear when thighs are pierced, basting every 10 minutes with glaze, about 55 minutes. Halve game hens, transfer to plates and serve.

Serves 8.