In a large bowl, cream together butter and sugar until smooth.
Beat in eggs and vanilla only until mixed.
Stir in the flour, baking powder, and salt. Cover, and chill dough for at least one hour (or overnight if you have time).
Preheat oven to 400 degrees.
Roll out dough on floured surface 1/4 to 1/2 inch thick. Cut into shapes.
Place cookies 1 inch apart on ungreased cookie sheets.
Bake 6 to 8 minutes in preheated oven.
Cool completely before frosting