Preheat your oven to 350°F. Line a large cookie sheet with parchment paper.
In a large mixing bowl, beat the softened butter and granulated sugar with an electric mixer until light and fluffy. Mix in the egg and anise extract until well combined.
Gradually add the flour, baking powder, and salt to the butter mixture, mixing until a soft dough forms.
Scoop out 1-½ tablespoons of cookie dough, roll them into balls, and place them on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the bottoms of the cookies are lightly golden. Let them cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.
Whisk together the powdered sugar and heavy cream in a small bowl until smooth. Once the cookies are cool, dip the tops in the icing, then set them on a wire rack until the icing hardens. For a festive touch, sprinkle colored sugar or nonpareils on top of the icing before it sets.
Serve at room temperature and store in an airtight container in the refrigerator.