In a medium bowl, whisk together flour, baking powder, and salt until evenly combined.
In the bowl of a stand mixer, cream butter and sugar on medium speed for 3–4 minutes, scraping the sides occasionally, until light and fluffy.
Beat in the egg, vanilla extract, and almond extract until the dough is smooth and uniform.
Gradually add the dry ingredients and mix until a soft dough forms. Divide the dough in half, flatten each into a 1-inch-thick disk, wrap in plastic, and chill for 1 hour.
Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper.
On a lightly floured surface, roll one disk of dough to 1/4-inch thickness. Cut into shapes and place cookies 2 inches apart on prepared sheets.
Bake for 8 minutes, rotating the pan halfway through, until the edges just begin to turn golden. Let cool on the pan for 2 minutes, then transfer to a wire rack to cool completely.
Meanwhile, whisk together powdered sugar, milk, and vanilla extract until smooth. Divide and color as desired.
Pipe or spread icing onto cooled cookies. Allow the icing to set at room temperature for 2 hours before serving.