Preheat the oven to 350°F. Using a heavy-duty mixer, beat the eggs at high speed until light and foamy, about five minutes. Set aside.
In a large bowl, combine the flour, confectioners' sugar and baking powder. On low speed, gradually beat in the shortening and extracts until the mixture resembles fine crumbs. Gradually add the beaten eggs. The dough will be stiff.
Roll the dough into 1-inch balls. Place the balls 2 inches apart on ungreased baking sheets. Bake for 12 to 14 minutes. The tops of the cookies will not brown, but the bottoms should brown slightly.
In a small bowl, combine the confectioners' sugar, milk and extracts until smooth. When you remove the cookies from the oven, quickly dip two or three cookies at a time into the glaze. Remove the cookies from the glaze with a slotted spoon or tongs. Place the dipped cookies on wire racks to drain. Immediately top with sprinkles. Let the cookies dry for 24 hours before storing them in airtight containers.
