Step 1: In a large mixing bowl, using an electric mixer, cream together the softened unsalted butter and granulated sugar until the mixture is light, fluffy, and pale in color. This usually takes about 2-3 minutes. Scrape down the sides of the bowl as needed to ensure everything is well combined.
Step 2: Beat in the large egg and the pure vanilla extract until just combined. Be careful not to overmix at this stage.
Step 3: In a separate medium bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and a soft dough forms. Do not overmix.
Step 4: Divide the dough in half. Flatten each half into a disk, wrap tightly in plastic wrap, and refrigerate for at least 1 hour, or up to 2 days. Chilling the dough is essential to prevent spreading and ensures cookies hold their shape.
Step 5: Preheat your oven to 375°F (190°C) and line baking sheets with parchment paper or silicone mats.
Step 6: On a lightly floured surface, roll out one disk of chilled dough to about 1/4-inch thickness. Use your favorite Christmas-themed cookie cutters to cut out shapes.
Step 7: Carefully transfer the cut-out cookies to the prepared baking sheets, leaving about 1 inch between each cookie. Re-roll any scraps, but avoid overworking the dough.
Step 8: Bake for 8-10 minutes, or until the edges are lightly golden. Baking time will vary depending on your oven and the size of your cookies. Watch them closely!
Step 9: Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
Step 10: In a medium bowl, whisk together the powdered sugar, milk, and pure vanilla extract until smooth and creamy. If the icing is too thick, add more milk a teaspoon at a time. If too thin, add more powdered sugar.
Step 11: Divide the icing into separate bowls if you plan to use different colors. Add a few drops of gel food coloring to each bowl and mix until the desired shade is achieved.
Step 12: Once the cookies are completely cool, spread the icing with a small offset spatula or knife, or use piping bags for intricate designs. Add sprinkles as desired.
Step 13: Allow the decorated cookies to set for at least 30 minutes to an hour, or until the icing is firm to the touch before storing.