Sift together the flour, baking powder, and salt in a medium bowl. Set aside.
Place the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment. Start the mixer on low, then gradually increase the speed to medium and continue to beat, scraping down the sides of the bowl as necessary until light and fluffy, 3 to 5 minutes, depending on the temperature of the butter. Add the egg, followed by the milk, and continue to beat on medium speed until smooth, about 30 seconds. Reduce the mixer speed to low, then gradually add the flour mixture, and beat until mixture comes together, about 30 seconds. Divide the dough in half, wrap each piece in plastic wrap, and refrigerate for 1 hour.
Heat the oven to 375°F with the oven racks in the upper middle and lower middle positions. Line two half sheet pans with parchment paper.
Use a small strainer or sifter to sprinkle your rolling surface with confectioners’ sugar. Remove 1 wrapped pack of dough from refrigerator, place on the sugar-dusted counter, and dust with a little additional sugar. Working quickly (so the butter doesn’t have time to melt), roll out dough to 1/4-inch thick, using pastry rulers if you so desire.
Cut the dough into your desired shapes using cookie cutters and place at least 1 inch apart on the prepared sheet pans. Re-roll the scraps one time and cut into additional shapes. Discard any remaining dough; do not re-roll a second time. Bake both pans of cookies, rotating the pans halfway through baking time, until the cookies are just beginning to turn brown around the edges, about 10 minutes. Leave on the pan for 2 minutes after removal from the oven and then move to a wire rack to cool completely.
While the first batch is baking, roll and cut the second half of the dough. Bake and cool the second batch, then decorate as desired. Serve.