Whisk together the all-purpose flour, baking powder, and salt in a medium bowl. Set aside.
In a large bowl using a hand mixer or a stand mixer fitted with the paddle attachment beat the unsalted butter and sugar together on high speed until completely light-colored and creamy, or for 3 minutes.
Add the egg and vanilla extract and beat on high speed until completely combined. Scrape down the sides with a silicone or rubber spatula and beat again as needed to ensure all ingredients are combined.
Add the dry ingredients to the butter mixture and mix on low until all the flour is just combined. Your dough will be soft; when you touch it, it won't stick to your fingers. If the dough seems too sticky to roll out, mix in one more tablespoon of flour.
Split the dough into 2 equal parts. Place each portion onto a piece of parchment paper or silicone baking mat that has been lightly dusted with powdered sugar. Sprinkle some powdered sugar on your rolling pin then roll the dough out to about ¼-inch thickness. The shape doesn't matter.
Cover the rolled-out dough with plastic wrap then refrigerate for at least 1 hour or up to 2 days.
Line 2-3 large baking sheets with parchment paper or silicone baking mats. Using cookie cutters, cut the dough into shapes. Re-roll the remaining dough (give it a quick chill in the freezer to ensure great cookies, no more than a couple of minutes) and continue cutting until all the dough is used. Repeat with 2nd rolled out dough.
Preheat oven to 350 degrees F (180 degrees C).
Arrange cut out cookies on baking sheets 2 inches apart. Give a quick chill in the freezer while the oven is preheating. The cooler the cookies, the better shaped they'll come out once baked.
Bake for 11-12 minutes or until lightly browned around the edges. Rotate the baking sheet halfway through the bake time to ensure even baking.
Allow cookies to cool on the baking sheet for 5 minutes then transfer to a wire rack to cool completely before decorating.
Royal Icing
In a large bowl of a stand mixer combine the egg whites and vanilla and beat until the egg whites are frothy.
Gradually add powdered sugar to the egg whites and mix on low speed until sugar is well incorporated and the mixture is shiny. Turn the speed up to high and beat until the egg whites form stiff, glossy peaks. This should take about 5-7 minutes.
If you want coloring in your icing, spoon small amounts of the icing into separate bowls and use gel food coloring sparingly.
Transfer icing to a piping bag and decorate the cookies. Store in an airtight container in the refrigerator for up to 3 days.
Once the icing has set, eat them or prepare them for gifting. The cookies stay soft for about 5 days covered tightly at room temperature or keep in an airtight container and refrigerate for up to 10 days.