Using a heavy-duty mixer, combine sugar, salt and eggs and beat on high speed until creamy.
Add milk, ice water and vanilla, and on low speed gradually add sifted flour, baking powder and nutmeg.
Add melted shortening and mix on low speed until thoroughly blended. Chill batter in refrigerator for eight hours.
Knead dough until pliable. Roll out and cut with a doughnut cutter. Re-roll dough using as little flour as possible.
In a deep-fat fryer, heat oil to 375° F.
Fry crullers until golden. Drain and cool to room temperature. Dust with superfine granulated sugar (or, confectioners’ sugar).