Sauté onion in oil in a large frying pan over medium heat, stirring occasionally, until soft, about 5 minutes.
Add port, 2 cups chicken broth, the figs, and star anise. Boil over medium-high heat, stirring occasionally, until liquid is reduced by about a third, about 15 minutes. Remove and discard star anise.
Purée mixture in a blender until smooth. Pour into a saucepan over low heat. Whisk in butter, vinegar, salt to taste, and a generous amount of pepper. If sauce is too thick, thin with a little more chicken broth. Serve hot.
Note: Nutritional analysis is per serving.