1. Sift together flour, baking powder and salt. Set aside.
2. In large mixing bowl, cream together butter and sugar until smooth. Beat in eggs, one at a time, and vanilla. Stir in flour mixture, taking care not to over mix. Cover and chill dough in refrigerator for at least two hours or overnight.
3. Preheat oven to 400 degrees F.
4. On pastry board dusted with confectioner's sugar, roll out dough to 1/4 inch to 1/2 inch thick. Cut out shapes with cookie cutters. Place cookies 1-inch apart on ungreased cookie sheet. Bake 6 to 8 minutes.
5. Let baked cookies rest on cookie sheet for 2 to 3 minutes. Transfer cookies to wire rack and cool completely. When cookies are completely cool, ice and decorate as desired.