Combine sugar and melted shortening in a large mixing bowl; mix well. Add eggs and milk; beat well.
Combine flour, baking powder, nutmeg, and salt; add to creamed mixture, stirring well. Turn dough out onto a heavily floured surface; roll to 1/4-inch thickness. Cut dough with a floured doughnut cutter.
Drop doughnuts, a few at a time, into deep hot oil (375°). Fry until golden brown, turning once. Drain doughnuts well on paper towels.
Split doughnuts in half crosswise. Place on baking sheets cut side up; brush with butter.
Broil 4 inches from heating element 2 minutes or until lightly browned. Sprinkle doughnut halves with powdered sugar, if desired.