Combine butter, sugar and vanilla in large bowl. Using a hand mixer, beat at medium speed until creamy. Add flour, baking powder, and salt and beat at low speed until well mixed. Wrap in plastic and refrigerate at least 2 hours or until firm.
When ready to bake, heat oven to 350°F. Roll out dough on lightly floured surface, one-third at a time (keep remaining dough refrigerated) to 1/4-inch thickness. Cut out and place about 1 inch apart on ungreased cookie sheets.
Bake 8 - 10 minutes or until edges are lightly browned. Cool for 1 minute on cookie sheet before removing to cooling rack. Cool completely before frosting.