Preheat oven to 350°. In a bowl, stir together flour and baking powder. In another bowl, beat butter with sugar until fluffy and light. Beat in eggs and vanilla. Stir in flour mixture, a third at a time to make a stiff dough. Divide dough into 4 pieces. Roll out a portion of cookie dough to 1/4 inch thick. Cut out shapes using cookie cutters. Place on lightly greased or nonstick cookie sheets. Bake until lightly golden, about 10 minutes, rotating baking sheet halfway through cooking time. Cool completely on pans about 5 minutes, transfer to cooling racks and cool completely before decorating.