Preheat the oven to 350 degrees F (175 degrees C).

Beat butter and sugar together in a large bowl with an electric mixer until smooth. Beat in egg and anise extract until combined.

Sift flour, baking powder, and salt together into a bowl. Stir into butter mixture until well incorporated. If you are using a stand mixer, mix dough another minute to add lightness. The dough will be soft, but will hand roll easily.

Pinch off pieces of dough slightly smaller than a walnut; roll into small logs. Dip in milk, then roll in sesame seeds. Place cookies one inch apart on a baking sheet. Cookies will not spread very much.

Bake in the preheated oven until bottom and sides of cookies are lightly toasted, 17 to 20 minutes. Transfer cookies to wire racks to cool. Store in an airtight container at room temperature.