Stir together flour, baking powder and salt on piece of waxed paper.
Beat together butter, margarine and sugar in bowl until creamy. Beat in egg and vanilla until well blended. Stir in flour mixture. Shape into disk; wrap in plastic wrap; refrigerate several hours or overnight.
Heat oven to 350°F. Coat baking sheet with nonstick cooking spray.
Roll out dough on lightly floured surface to 3/8-inch thickness. Cut into rounds with 2-1/2-inch cookie cutter; reroll scraps. Place on prepared baking sheets, spacing 1-1/2 inches apart.
Bake in 350°F oven 10 to 12 minutes or until lightly browned at edges. Remove cookies to wire rack to cool.