Mix together yeast, warm water, potato water, sugar, and 1 cup of flour. Set until bubbly (yeast dissolved)
Add mashed potatoes, 5 cups of flour, nutmeg, butter, and eggs. For flour, add 3 cups, stir with beater, then add the last 2 cups and stir with dough hook.
Mix well and knead more flour in if needed. The dough should be light and a little sticky.
Let rise to double in a bowl.
Roll out 1/3 inch thick on floured board and cut out (in bars or round shapes). Place on cookie sheet and let rise again.
Fry in hot canola oil 2.5 inches deep. Grandma always turned her doughnut over as soon as she put them into the oil, then let each side brown.
Roll in sugar (granulated or powdered sugar), or frost with frosting after doughnuts are cool.
Sift together the sugar and cocoa powder in a medium bowl. Slowly stir in the milk and vanilla, a little at a time, to make a smooth, pourable glaze.
Whisk together the icing ingredients. Dip the dome-iest side of the doughnuts into the icing and spread it out if necessary. Allow to stand for 10-15 minutes before serving.
Combine milk and vanilla in a medium saucepan and heat over low heat until warm. Sift confectioners’ sugar into milk mixture. Whisk slowly, until well combined. Remove the glaze from the heat and set over a bowl of warm water. Dip doughnuts into the glaze, 1 at a time, and set on a draining rack placed in a half sheet pan for 5 minutes before serving.