In a large bowl, mix butter and white sugar till smooth. Add powdered sugar, eggs, and vanilla. Mix well.
Sift flour, baking powder, and salt in a small bowl. Add flour mixture to butter mixture slowly. Mix well.
Cover, and chill dough for at least one hour or overnight.
Preheat oven to 350 degrees F. Roll out dough on powdered sugared surface (you can use flour too). Roll out dough to 1/4 to 1/2 inch thick. Cut into shapes with any cookie cutter. Place cookies 1 inch apart on ungreased cookie sheets.
Bake 7-9 minutes in preheated oven. Cool completely.