Preheat oven to 400°
In the large bowl with a mixer, cream together butter and powdered sugar, and mix until the butter is light in color and well blended.
Mix in the egg and vanilla.
Blend in 2 3/4 cups flour, baking powder, and salt. (only add the additional 1/4 cup flour if needed, the dough should be supple and soft not dry)
Mix until the dough forms a ball, on medium speed.
Roll out cookie dough in between wax paper sheets, or lightly floured surface.
Roll out cookie dough to 1/4" thick.
Dip cookie cutter into flour and press evenly into cookie dough, then transfer to a parchment-lined baking sheet.
Bake in a well preheated oven at 400° for 7-9 minutes, until the cookies are golden on the bottom, but the tops are not browned yet.
Cool completely before icing.