Preheat the oven to 375 degrees F (190 degrees C). Grease or line cookie sheets.

Combine flour, sugar, and baking powder together in a large bowl. Make a well in the center and add oil, milk, eggs, and 1 tablespoon anise extract; mix together to form a workable dough. Roll dough into walnut-sized balls, flatten slightly, and place 1 inch apart onto prepared cookie sheets.

Bake in the preheated oven until edges are golden, about 8 minutes.

Meanwhile, make the icing: Mix confectioners' sugar, hot water, and 1 teaspoon anise extract together until smooth. Spoon or drizzle over warm cookies and allow to cool completely.