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1
Have ready 2 parchment-lined baking pans.
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2
Place the potatoes in a small saucepan, cover with cold water, and bring to a boil over high heat.
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3
Cook until tender, about 15 minutes.
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4
Drain in a colander.
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5
Pass the potatoes through a potato ricer or food mill and into a medium bowl; set aside.
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6
Place 1/4 cup warm water in a small bowl; sprinkle with the yeast, stir gently, and let stand until creamy, 5 to 10 minutes.
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7
Using an electric mixer fitted with the paddle attachment, combine the milk, shortening, 1/4 cup sugar, and salt.
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8
Let stand until cooled to just warm.
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9
Add the yeast mixture, reserved potatoes, and eggs; beat until combined.
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10
Switch to the dough hook.
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11
Add 5 cups flour, and mix on medium-low speed until combined, adding more flour if necessary, until a smooth and elastic dough is formed, about 5 minutes.
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12
Transfer the dough to a large, lightly greased bowl; cover.
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13
Let stand in a warm place until the dough is doubled in size, about 55 minutes.
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14
Transfer the dough to a lightly floured surface.
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15
Roll out to 1/2 inch thick.
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16
Using a 2 1/2-inch-diameter doughnut cutter, cut and place on prepared baking pans.
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17
Loosely cover with plastic wrap; let stand in a warm place until the dough has risen by about one-third, about 30 minutes.
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18
Combine the confectioners sugar, vanilla, and remaining 6 tablespoons water in a medium bowl, stirring until smooth; set aside.
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19
In a medium bowl, whisk together the remaining 1/2 cup granulated sugar and cinnamon until well combined; set aside.
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20
In a large, low-sided saucepan over medium heat, heat the oil until a deep-fry thermometer registers 375F.
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21
Drop the doughnuts into the oil; fry in batches until golden, 1 to 2 minutes per side.
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22
Transfer to several layers of paper towel to drain.
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23
Place the drained doughnuts on a wire rack set over a baking pan.
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24
Dip half the doughnuts in the glaze; return to the wire rack.
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25
Roll the remaining doughnuts in the cinnamon-sugar mixture until well coated.
