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1
In a small saucepan, warm the milk, vanilla seeds and 1 tablespoon of the sugar over moderate heat until the temperature registers 105 on a candy thermometer.
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2
Transfer to the bowl of a standing electric mixer fitted with the dough hook.
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3
Add the yeast and let stand until foamy, 5 minutes.
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4
Add the shortening, egg yolks and remaining 1/2 cup of sugar and beat at medium speed just until the shortening is broken up.
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5
Beat in the salt, baking powder and mace.
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6
At low speed, add the flour, 1 cup at a time, until the dough is firm but still tacky (you may need to add more or less flour to achieve the desired consistency).
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7
Transfer the dough to a lightly floured work surface and knead a few times; pat it into a disk and transfer to a floured baking sheet.
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8
Dust with flour and cover with a towel.
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9
Place the baking sheet in the center of a turned-off oven.
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10
Set a large roasting pan on the bottom rack and fill it halfway with boiling water.
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11
Close the oven door and let the dough stand until doubled in bulk, about 1 hour.
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12
Line 2 baking sheets with wax paper and dust with flour.
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13
Turn the dough out onto a floured work surface and roll out to a 12-inch round, 1/2 inch thick.
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14
For doughnuts, use a floured 2 3/4-inch doughnut cutter (or 2 3/4-inch and 1 1/4-inch cookie cutters) and stamp them out as close together as possible; alternatively, for doughnut holes, use a 1-inch cookie cutter.
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15
Transfer the doughnuts and/or holes to the baking sheets and return to the oven.
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16
Refill the roasting pan with boiling water and close the oven door.
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17
Let stand until the dough has doubled in bulk, 45 minutes.
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18
Set a rack on a baking sheet and cover with paper towels.
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19
In a large saucepan, heat 2 inches of oil to 365.
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20
Add 3 or 4 doughnuts at a time; adjust the heat to keep the oil between 350 and 360.
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21
Fry the doughnuts until golden brown, 1 minute per side.
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22
If frying doughnut holes, cook them in batches of 12.
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23
Using a slotted spoon, transfer the doughnuts to the paper towels.