Heat the oven to 350°F and line two baking sheets with parchment. Beat butter and granulated sugar for 2 minutes, then beat in eggs, anise and vanilla.
Whisk flour, baking powder and salt. Mix into the butter with the dough milk just until a soft dough comes together.
Divide into 30 portions. Roll each into a short 4-inch rope, tie into a loose knot and place 2 inches apart on the sheets.
Bake one sheet at a time for 11 to 12 minutes, until the bottoms are lightly golden and the tops feel set. Cool completely on a rack.
Whisk powdered sugar and glaze milk until smooth. Dip the tops in glaze, add the measured sprinkles and let dry for at least 45 minutes before stacking.