In a bowl, combine 1 cup sugar, salt, nutmeg, vanilla and butter. Add potatoes; mix well. Add eggs and milk; mix well. Stir in the flour and baking powder. Chill thoroughly. On a lightly floured surface, roll out half the dough to 1/2-in. thickness. Cut into 4x1-1/2-in. strips; roll in flour and tie into knots. Preheat shortening or oil to 375°; fry doughnuts until golden on both sides, turning with a slotted spoon. Drain on paper towels. Repeat until all doughnuts are fried. Combine remaining sugar and cinnamon; roll warm doughnuts in mixture. Serve immediately.