In a 1 to 1 1/2 quart heavy saucepan bring anise, sugar, butter and vinegar to a boil over moderate heat, stirring, and boil 1 minute. Remove pan from heat and stir in flour and a pinch of salt until mixture is smooth. Col dough to room temperature.
Preheat oven to 350 degrees and line 2 large baking sheets with parchment paper.
Roll 1/2 tsp. of dough into balls and arrange 4 inches apart on baking sheets. Bake cookies in batches in upper and lower thirds of oven, switching position of sheets halfway through baking, 10 minutes, or until cookies are flat and golden. Transfer parchment with cookies to racks to cool. Cool baking sheets and line with fresh parchment between batches.