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1
Combine the yeast, warm water, and 1/2 teaspoon of the sugar in a small bowl.
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2
Set aside until the mixture becomes foamy, about 20 minutes.
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3
In the bowl of a standing electric mixer, beat the egg with the remaining 1/3 cup sugar and the salt until the mixture is thick and light.
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4
Beat in the yeast mixture, the scalded milk, and the butter, and gradually add enough flour to form a soft dough.
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5
Knead the dough on a floured surface for 1 minute, just until it is smooth and elastic, and form it into a ball.
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6
Put the dough in a buttered bowl, cover with plastic wrap, and let it rise in a warm place for 1 hour and 30 minutes, or until it has doubled in bulk.
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7
When the dough has risen, punch it down, and on a floured surface roll it out 1/3 inch thick.
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8
With a 2 1/2-inch cutter dipped in flour, cut out rounds.
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9
With a 1-inch round cutter dipped in flour, cut out and reserve the centers from the rounds.
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10
Gather the scraps gently into a ball, reroll the dough, and cut out doughnuts and holes in the same manner.
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11
With a spatula, transfer the doughnuts and holes to a baking sheet sprinkled lightly with flour, and let rise, uncovered, in a warm place for 30 minutes to 1 hour, or until they have doubled in height.
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12
In a large deep fryer, heat 3 inches vegetable shortening or vegetable oil to 360F.
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13
Fry the doughnuts, four at a time, for 1 minute on each side, or until they are golden brown and puffed, then transfer them with a skimmer to paper towels to drain.
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14
Fry the doughnut holes separately, turning them to brown evenly.
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15
Dip the doughnuts and holes, one at a time, in the icing, turning them to coat them, and transfer them with tongs to a rack set over waxed paper to dry.
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16
In a small bowl, combine the confectioners sugar and 4 tablespoons of the milk; stir well.
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17
Add additional milk to reach the desired consistency.
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18
Stir in the maple extract.
