5 cups all-purpose flour, plus more, if needed, for the dough and work surface
2 quarts vegetable oil, plus more for the bowl
4 cups confectioners’ sugar
1 teaspoon pure vanilla extract
1/2 teaspoon ground cinnamon
Have ready 2 parchment-lined baking pans.
Place the potatoes in a small saucepan, cover with
cold water, and bring to a boil over high heat. Cook
until tender, about 15 minutes. Drain in a colander.
Pass the potatoes through a potato ricer or food
mill and into a medium bowl; set aside.
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. Using an electric mixer fitted
with the paddle attachment, combine the milk,
shortening, 1/4 cup sugar, and salt. Let stand until
cooled to just warm. Add the yeast mixture, reserved
potatoes, and eggs; beat until combined.
Switch to the dough hook. 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. Transfer the
dough to a large, lightly greased bowl; cover. Let
stand in a warm place until the dough is doubled
in size, about 55 minutes.
Transfer the dough to a lightly floured surface.
Roll out to 1/2 inch thick. Using a 2 1/2-inch-diameter
doughnut cutter, cut and place on prepared baking
pans. Loosely cover with plastic wrap; let stand in
a warm place until the dough has risen by about
one-third, about 30 minutes.
Combine the confectioners’ sugar, vanilla, and
remaining 6 tablespoons water in a medium bowl,
stirring until smooth; set aside. In a medium bowl,
whisk together the remaining 1/2 cup granulated
sugar and cinnamon until well combined; set aside.
In a large, low-sided saucepan over medium heat,
heat the oil until a deep-fry thermometer registers
375F. Drop the doughnuts into the oil; fry in
batches until golden, 1 to 2 minutes per side. Transfer
to several layers of paper towel to drain. Place
the drained doughnuts on a wire rack set over a baking
pan. Dip half the doughnuts in the glaze; return
to the wire rack. Roll the remaining doughnuts in
the cinnamon-sugar mixture until well coated.