In a large bowl, cream together butter and sugar until smooth. Beat in eggs and vanilla. Stir in flour, baking powder and salt. Cover dough with plastic wrap and chill in refrigerator for at least one hour, or overnight.
When ready to bake, preheat oven to 400 degrees F. Line a baking sheet with parchment paper. Roll out cookie dough directly on ungreased, lined baking sheet to 1/4-inch thickness. If dough becomes sticky while rolling, lightly dust with powdered sugar. Cut into shapes with desired cookie cutter and peel away excess dough.
Bake 6 to 8 minutes in preheated oven. Cool completely.
Royal Icing
In a large bowl, mix all ingredients on low speed for 7-10 minutes, or until icing forms peaks.
Cover the bowl with a dampened towel to prevent crusting and drying.
Tint with food colorings or thin the icing with small amounts of warm water to reach the desired consistency.