For the cookies:In a bowl, stir together flour, semolina, baking powder, baking soda and salt.
In a spouted measuring cup, whisk together the egg, yolks, sambuca and anise extract.
In a mixer fitted with the paddle attachment, cream the butter and sugar until the combination is light and fluffy (about 2 minutes).
Add the egg-yolk mixture to the mixer and beat on medium until smooth.
Add the flour mixture and beat on low just until combined.
Remove dough from mixing bowl, wrap it with plastic and chill it until firm (about 1 hour).
Preheat the oven to 350 degrees.
Roll the dough into four dozen balls and bake in batches on parchment-lined sheet pans.
Bake 16 to 18 minutes or until golden.
Rotate the pans from the top to bottom racks in your oven halfway through the baking time.
For the glaze:Whisk the milk and anise extract into the confectioners' sugar to make a smooth glaze about the thickness of pancake batter.
Add a little more milk or confectioners' sugar to adjust the consistency.
Dip or drizzle the cookies with glaze and let set on a rack.