Preheat the oven to 350F. Line a small baking sheet or tray with wax or parchment paper.
In a medium bowl, whisk together flour, baking powder, and salt. In a large mixing bowl, beat butter and sugar together on medium speed until light and fluffy, about 3 minutes. Add the eggs, one at a time, beating until incorporated before adding the next. Stop to scrape down the bowl as needed. (Mixture will be runny and look lumpy.) Beat in the anise.
Add the flour mixture, and beat on low speed just until combined. Scoop dough by 1 tablespoonful and place on a lined tray. Chill for 20 minutes or until firm enough to roll between your palms. Roll half of the dough scoops into smooth balls and place on a parchment-lined baking sheet about an inch apart. Keep the remaining dough refrigerated.
Bake for 10 minutes or the cookies firm to the touch and the tops appear dry. Let cool completely on the baking sheets.
For the Glaze:
Sift powdered sugar into a medium bowl. Whisk in the milk. Spoon about 1 teaspoon of glaze onto the top of each cookie. Decorate with sprinkles if desired. (The glaze sets fast, so either work quickly or glaze half and sprinkle before continuing.) Keep them on the parchment until the glaze is set, about 2 hours.
Notes
Adding too much flour will lead to the cookies being dense. The best and easiest way to measure the flour is by using a kitchen scale. If you don’t have one, then fluff your flour with a spoon, sprinkle it into your measuring cup, and use a knife to level it.
I highly recommend using a cookie scoop. Using a cookie scoop ensures that all the anise cookies are the same size so that they bake evenly. If you plan on baking cookies regularly, it’s worth purchasing!
Room temperature butter and egg will mix more evenly into each other. Place your egg into a bowl of warm water for a couple of minutes. Doing so will quickly bring it to room temperature if you have forgotten to take it out of your fridge beforehand.
Be sure to let the anise cookie dough chill before you bake. This will prevent the cookies from spreading too much.
Don't worry if some of the cookies crack on top when baking. The glaze will cover them!
Not a fan of anise? Sub vanilla extract in its place or use ½ teaspoon almond, lemon, or peppermint extract instead.