My family isn't Italian, so when I had my first Italian Anise Cookie, I was in my 20's. Christmas hasn't been the same ever since.
Preheat oven to 350ºF. Line 2 baking sheets with parchment paper.
Whisk together the sugar, oil, anise, and milk. In another bowl, whisk together the flour, baking powder and salt. Add the wet ingredients to the dry and mix until blended. The dough should be somewhat loose, if it’s not, add a little more non-dairy milk.
Drop dough by rounded teaspoon, 2 inches apart onto prepared baking trays and bake for 10 to 14 minutes or until bottoms of cookies are light golden. Do not over bake. Cool on wire racks.
To make the icing, mix the sifted powdered sugar, non-dairy milk and anise in a small bowl until smooth. It’s important to use sifted powdered sugar or your icing will have visible lumps in it. The icing should be thick but pourable from a teaspoon. Adjust the liquid to get the right consistency.
Place a piece of parchment under the cooling rack so that the glaze can drip through, then spoon it gently over the cookies so that it drips down the sides and nearly covers the whole cookie. While the icing is still wet, sprinkle with colored sugar or nonpareils. Let icing dry for about an hour before serving.