Add the powdered sugar, salt, potato, and hot water to the foamed yeast along with 1/4 cup all-purpose flour and 1/4 cup cake flour and mix on low to combine with a paddle. Mix on high-speed 30 seconds to combine. Add another 1/4 cup all-purpose flour and mix on high.
Flour the bench heavily and knead the dough gently (it may be sticky). Turn into a greased bowl and proof until doubled in bulk, about 1 1/2 hours. Turn dough out onto a floured surface and punch down. In a bowl proof the dough another 30 minutes.
Flour surface heavily and pat dough out to about 1/2-inch thick. Cut out doughnut holes, flouring cutter each time, and set on a floured sheet pan.
Heat oil to 375 degrees F.
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