Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a medium bowl, whisk together the flour, baking powder, and salt.

In a large bowl, beat the eggs and granulated sugar using a hand mixer or stand mixer until light and fluffy.

Add the melted butter, 2 teaspoons of anise extract, and 1/4 cup of milk to the egg mixture and mix until combined.

Gradually add the dry ingredients to the wet ingredients, stirring until a soft, slightly sticky dough forms.

Scoop tablespoon-sized portions of dough and roll into 1-inch balls, placing them 2 inches apart on the prepared baking sheets.

Bake for 8 to 10 minutes, or until the bottoms are lightly golden but the tops remain pale.

Transfer the cookies to a wire rack and allow them to cool completely before glazing.

In a small bowl, whisk together confectioners' sugar, 3 tablespoons of milk, and 1/2 teaspoon of anise extract until a smooth glaze forms.

Dip the top of each cooled cookie into the glaze, let excess drip off, and immediately top with nonpareil sprinkles before the glaze sets.