In small sauce pan heat the 1/4 cup shortening until melted. Set aside to cool slightly but remain liquid.
In a standing mixer fitted with the paddle attachment, beat the sugar and melted shortening together on medium speed, until just combined. Add the eggs, one at a time, beating well after each addition. Add the milk and vanilla, continue beating until the mixture is light, about 2 minutes.
Sift the flour, baking powder, nutmeg, mace, and salt into a medium bowl. Add the flour mixture to the egg mixture on low speed until just combined. The texture of the dough will be soft and loose. Remove bowl from the mixer, scrape the dough off the paddle blade with a spatula. Transfer the dough to a large piece of plastic wrap and wrap it well. Refrigerate the dough for 4 hours or overnight.
Roll the chilled dough out about 1/2 inch thick on a very lightly dusted workspace. Dip the edges of a 2 1/2-inch doughnut cutter in flour and cut the dough into doughnuts. Place the donuts and holes on a baking sheet lined with parchment.
Spoon enough vegetable shortening into a tall heavy-bottomed pot so it fills the pan a third of the way. Heat the shortening over medium heat until a deep frying thermometer set in the oil registers 375 degrees F. Line a baking sheet with paper towels.
Working in batches, fry the doughnuts and holes, turning once, until they are golden brown, about 2 minutes. Transfer the doughnuts from the fat with a slotted spoon or skimmer to the paper towels to drain and cool. Repeat until all the donuts and holes are fried. Make sure the oil comes back to the correct temperature before frying each batch.
For sugared doughnuts, roll the doughnuts in sugar or cinnamon sugar while they are still warm. For confectioners' sugared covered doughnuts allow the doughnuts to cool completely before rolling in the confectioners' sugar.
These are best just after making.
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