In a large mixing bowl, beat the softened butter and granulated sugar together on medium speed until the mixture is pale, light, and fluffy, which usually takes about 3 minutes.
Add the egg and vanilla extract to the butter mixture, beating until fully incorporated and smooth.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients while mixing on low speed, stopping as soon as the flour streaks disappear to avoid overworking the dough.
Divide the dough into two disks, wrap them tightly in plastic wrap, and refrigerate for at least 1 hour to firm up the fats.
Preheat your oven to 175 degrees Celsius (350 degrees Fahrenheit).
Roll out one disk of dough on a lightly floured surface until it is approximately 6 millimeters thick.
Use your preferred cookie cutters to cut out shapes and place them onto a parchment-lined baking sheet, spacing them 3 centimeters apart.
Bake for 10 to 12 minutes, or until the edges are just barely turning a pale golden color; the centers should still look soft.
Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely before icing.