In large bowl, mix flour, baking powder and white sugar. Make a well in the center and add oil, milk, Ouzo, and eggs. Mix together until dough is sticky
Rest the dough for 20 minutes to allow hydration.
Oil fingers and pinch off dough in 1 inch pieces. Roll into a ball and place on a lightly greased cookie sheet, 1 inch apart, flatten top slightly. Bake for 8 minutes.
Glaze
Blend in anise extract and enough hot water to confectioner's sugar to form a smooth icing. Adjust water for a "Coat the back of a spoon" thickness. Ice cookies whilst warm
Notes
Going a bit farther one can add the zest of one lemon and the juice of 1/2 of said to the cookie dough for a stronger Italian influence.