Preheat oven to 350 °F with a rack in the center. Whisk together flour with baking powder and salt in a small bowl and set aside.
Using a stand-up or handheld mixer, beat the butter together with sugar. To the mixture add vanilla extract and egg and beat to combine.
To the butter mixture, add flour in 3 parts until fully incorporated.
Divide the dough into two equal parts. On a lightly floured surface, roll into ¼-inch thickness. Use a cookie cutter to cut out your favorite shapes.
Bake cookies on a parchment or silicone-lined baking sheet at 350˚F for 10 minutes, or until the edges are just beginning to turn golden. Let the cookies cool for about 5 minutes on the baking sheet before moving them to a wire rack to cool completely and decorating with cookie icing.