Cream the butter and sugar together until light and fluffy. Blend in eggs and beat well. Sift together flour and baking powder; add to creamed mixture. Add milk and vanilla; mix well.
Cover and chill for 1 to 2 hours.
Roll very thin. Cut with cookie cutter dipped in flour. Place on greased cookie sheet. Bake at 400 degrees F (200 degrees C) for 6 to 8 minutes.
