Sift the flour, baking powder, and salt into a large bowl.
In a separate large bowl, combine the sugar and room-temperature unsalted butter with an electric hand mixer or stand mixer on low speed. Then, add the egg, vanilla extract, milk of choice, and combine.
Add the dry ingredients to the bowl with the wet ingredients a little at a time until fully incorporated. Use your mixer and make sure the dough is thoroughly combined.
Form your cookie dough into a flatter piece that is about 1-2 inches thick so it is easier to roll later. Think of a thick round pizza dough shape. Wrap your cookie dough in plastic wrap Then, chill the cookie dough in the refrigerator for 1-3 hours or overnight. You can place it in a small sheet pan in the refrigerator if that helps. If you chill the dough overnight, allow about 20 minutes before rolling.
Remove your chilled dough from the refrigerator and place it on your work surface. Sprinkle some flour on your work surface so the dough doesn’t stick. Then, roll out your dough with a rolling pin. Make sure the dough is the same thickness throughout. If you would like softer cookies, roll the dough a little thicker, and roll it thinner if you want crispier cookies. Our dough was about 1/4 inch in thickness.
Once the dough is rolled out, use cookie cutters to make sugar cookies. Keep re-rolling the extra dough left over around the cut cookies. Repeat until all of your dough is used. This recipe makes 28-32 regular-sized cookies, depending on the size of the cookie cutters used.
Place the cookies on a sheet pan with parchment paper. Bake them at 350°F for 9-12 minutes depending on size, thickness, and softness desired. Make sure not to overcook them. They are done when they are lightly brown around the edges.
Once cooked, let your cookies cool on a wire rack. Once cooled, combine the powdered sugar, vanilla extract, and milk of choice to form your icing. Optional: Place some icing in separate bowls and add a few drops of edible food coloring to each bowl to make different colored icings. Once ready, place your cookies on a cooling rack and drizzle the icing over your cookies to decorate them. Decorate to your liking, let the icing dry, and enjoy!