Sift flour, baking powder, and salt into a bowl. In a separate bowl, beat butter and sugar with a mixer on medium speed until pale and fluffy, about 3 minutes. Beat in eggs and vanilla. Reduce speed to low. Gradually mix in flour mixture. Turn out dough, and divide in half. Flatten each half into a disk, and wrap in plastic. Refrigerate until firm, at least 1 hour or overnight.