For cookies: Preheat oven to 375°. Line two baking sheets with parchment paper.Advertisement
In a large bowl, beat sugar, butter and shortening with an electric mixer on medium-high speed until light and fluffy, about 2 minutes, scraping sides and bottom of bowl occasionally. Beat in eggs, 11/2 teaspoons anise extract and the vanilla until combined, scraping bowl occasionally. Reduce speed to low and beat in flour, baking powder and 1/2 teaspoon salt.
Shape dough into 1-inch balls and arrange 2 inches apart on prepared baking sheets. Bake until bottoms just begin turning golden, about 8 minutes. Transfer cookies to wire racks to cool.
For icing: In a medium bowl, whisk together powdered sugar, lemon juice, 1/4 teaspoon anise extract and a pinch of salt. Add more lemon juice as needed to create an icing that falls from the whisk in a thin ribbon. Working with two cookies at a time, dip the tops into icing to coat completely. Place on wire racks set over wax paper. Sprinkle with colored sugar while icing is still wet. Let stand until glaze is completely set. Layer cookies between sheets of wax paper in an airtight container. Store in a cool place up to one week.
Anise extract (not anise oil, which is too strong), is the traditional flavoring in these long-lasting cookies, but lemon and almond extracts are just as popular.
Light-color baking sheets work better than dark ones to avoid burning cookie bottoms.