In a large bowl or stand mixer fitted with a paddle attachment, cream together butter and sugar on high until light and fluffy.
Add egg and vanilla and beat until well combined.
In a separate bowl, sift together flour, baking powder, and salt.
Slowly add the flour mixture to the butter mixture, lightly mixing between each addition until flour in completely incorporated.
Roll into a ball, divide in half, then shape each half into a disc and wrap them in cling wrap and chill for 2 hours.
Preheat oven to 375°F.
Roll dough out to ¼ inch thickness on a lightly floured board.
Flour or spray cutter with cooking spray.
Place cookies on a parchment-lined baking sheet and bake for 8-10 minutes.
Let cool completely before icing.