In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
Beat eggs and sugar on medium-high speed for 3 minutes until pale and thickened.
Reduce mixer speed to low and add melted butter, milk, anise extract, vanilla extract, crushed anise seeds, and lemon zest. Mix for 30 seconds.
Gradually add the flour mixture in three batches, mixing just until incorporated.
Cover the bowl and let the dough rest at room temperature for 30 minutes.
Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
Scoop tablespoon-sized portions of dough onto prepared sheets, spacing 2 inches apart.
Bake one sheet at a time for 10-12 minutes until edges are barely golden.
Cool on baking sheet for 5 minutes before transferring to wire rack.
Make glaze by whisking confectioners' sugar, milk, and anise extract until smooth.
Dip tops of cooled cookies in glaze and add sprinkles if desired.
Allow glaze to set completely for 1-2 hours before storing.