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1
To make the donuts:
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2
Boil the potatoes until fork tender. Set aside the cooking liquid. Push the potatoes through a food mill or mash by hand, leaving no lumps. Measure out 3/4 cup of mashed potatoes.
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3
In the bowl of a stand mixer, combine the mashed potatoes with 1/2 cup of flour and the egg.
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4
In a small pot, heat the 3/4 cup of potato water, sugar, butter, and salt over low heat until the butter has melted. Stir this mixture into the potato mixture and blend until smooth.
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5
Dissolve the yeast in the remaining 2 tablespoons of warm potato water. Add to the potato mixture. Mix in the mace and nutmeg and mix thoroughly.
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6
Add remaining flour a little at a time, with your mixer on low and fitted with the dough hook, until a stiff dough forms. Continue kneading until smooth and elastic.
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7
Remove dough to a greased bowl and place in a warm spot to rise until doubled in bulk, about one hour.
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8
Turn the dough onto a floured surface and roll to 1/2 inch thickness. Cut the dough with a floured biscuit or donut cutter. (I find this dough to be pretty soft, so I use a biscuit cutter since it's easier to move the full circle around than it is to move around the donut shape.).
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9
Cover and let rise until doubled in bulk, about 45 minutes.
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10
Heat a deep skillet or pot with 2 inches of oil to 375 degrees. Fry the donuts in batches (don't overcrowd the pan), flipping as needed until golden brown on both sides.
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11
Drain a paper towel lined plate.
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12
To make the glaze:
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13
Heat the milk in a small saucepan until warm. Remove from the heat and stir in the powdered sugar and vanilla. Whisk together to form a glaze. Dunk the warm donuts in the glaze. Let sit for 5 minutes to set.
