In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
Place the butter and sugar into a separate large bowl. Use an electric mixer (stand or handheld) to cream the ingredients together on low speed until light and fluffy (about 3-5 minutes).
Next, add the egg and vanilla. Continue to beat on low speed until just combined.
Pour in the dry ingredients, and mix on low speed until a soft dough begins to form. The dough will be sticky and tacky but should hold it’s shape when pressed together.
Form the dough into disc shape and wrap with plastic wrap. Refrigerate the dough for at least 1-2 hours or overnight before making cookies.
When you’re ready to begin rolling out the cookie dough, line a cookie sheet with parchment paper, and preheat the oven to 350°.
Remove the dough from the refrigerator and place on a lightly floured surface. If the dough is firm and cracks around the edges as it’s being rolled, allow it to rest for 10-15 minutes. This will bring the temperature of the dough up enough to be handled with ease.
Continue rolling the dough until it reaches ¼ inch thick (⅛ inch for crispier cookies). Use a metal cookie cutter to press shapes into the dough and jiggle slightly to ensure the cutout is free on all sides.
Carefully place the cookie cutout onto the cookie sheet. Repeat until all the dough has been used. I was able to get 18 cookies that were ¼ inch thick and 3 inches in length. However, the size and thickness of the cookies will determine how many this dough makes.
Place the cookie sheet in the oven, and bake for 8-10 minutes or until the edges of the cookies begin to brown slightly.
Remove the cookies from the oven and transfer to a cooling rack. While the cookies cool, make the buttercream frosting.