1Heat the oven to 375°F and arrange the rack in the middle. Coat a baking sheet with margarine or line it with parchment paper and set aside. In the bowl of a stand mixer fitted with a paddle attachment, beat margarine, eggs, and sugar together on medium speed until creamy.
2Sift flour, salt, and baking powder slowly into margarine mixture. Beat until thoroughly incorporated. (Dough should be stiff enough to roll out.)
3Turn dough onto a floured surface and knead briefly. Divide into 3 pieces and form into flat disks; wrap 2 disks in plastic and chill in the refrigerator while working with the first disk.
4Using a floured rolling pin, roll first disk out to 1/4- to 1/8-inch thickness (if dough is not workable, place in the refrigerator for an hour). Cut out cookies using cutters dipped in flour, and arrange on the prepared baking sheet.
5Brush cookies with egg white, and sprinkle with sugar and sprinkles. Bake until lightly brown on edges, about 8 minutes.
6Remove from the baking sheet to a rack and let cool. Store in an airtight container with parchment or waxed paper between the layers.