For the cookies:
Preheat oven to 375°F. Line a baking sheet with parchment paper or a silpat. Set aside.
In a medium bowl, whisk together flour, baking powder and salt. Set aside.
In a stand mixer, beat butter and sugar until light and fluffy. Add egg and almond extract, mixing until combined. Add flour mixture 1/2 cup at a time, mixing until completely combined.
Roll 1 tablespoon of dough into small circles and then press with hands (or with the bottom of a cup) into a disk shape. Place on prepared baking sheet.
Bake for 8 minutes. The cookies will not look browned or cooked, but they are! Remove from oven and let cookies rest on baking sheet for 5 minutes. Then, transfer to a wire rack to cool completely.
In a small bowl, whisk together powdered sugar, milk and almond extract – until smooth.
Using a spoon, smooth icing onto the top of each cookie and let set for 10 minutes, or until hardened. Store in the fridge, let come to room temperature when ready to serve.