In a medium bowl, stir together the flour, baking powder, and salt.
In the bowl of an electric mixer, using the paddle attachment, cream together the butter and sugar until light and fluffy.
Add the egg and vanilla and beat another minute or so. Add the flour mixture slowly. Blend until all of the flour is incorporated.
Remove about half of the dough from the bowl and knead by hand just a bit to form a smooth ball. Roll out dough onto a lightly floured work surface, or onto a piece of plastic wrap.
Cut out cookies into desired shapes and place the entire baking sheet of unbaked cookies into the freezer for 5 minutes. Then, bake cookies.