Preheat oven to 325 degrees. Line baking sheets with parchment paper or non-stick foil.
Beat the sugar, melted butter, eggs, milk and anise extract together using low speed of a hand-held mixer.
Thoroughly stir together the flour, baking powder and salt; add to the batter and stir just until blended.
Drop dough by rounded teaspoons, shaping a little to form nice roundes, 2 inches apart onto cookie sheets and bake on center rack for 10 to 14 minutes or until bottoms of cookies are light golden. Cool on wire racks.
Make icing. Mix the sugar and melted butter together until the sugar is moist. Add the milk and beat well until smooth. Beat in the anise extract. It should be thick but pourable. Place a piece of paper towel under your cooling rack so that the glaze can drip through, then spoon it gently over the cookies.
