In a bowl, combine yeast, warm water and sugar to dissolve. Add 1/4 cup of the all-purpose flour and 1/4 cup of the cake flour. Stir and set in a warm place for 30 minutes to foam up. Combine cocoa powder and baking soda and add hot water to dissolve. Add the melted chocolate to the cocoa powder mixture then stir in the powdered sugar, salt, and potato. Add this to the foamed yeast along with another 1/4-cup of all-purpose flour and the remaining 1/4-cup of cake flour and mix on low to combine with a paddle.
Mix on high speed for 30 seconds to combine. Add the remaining 1/4-cup of all-purpose flour and mix on high speed. Flour the work surface 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 then proof for another 30 minutes.
Flour work surface heavily and pat out dough to about 1/2-inch thick. Cut out doughnuts and holes, flouring the cutter each time, and set on a floured sheet pan. Heat oil to 375 degrees and drop in doughnuts and holes. Cook doughnuts for 45 to 60 seconds and the holes for 30 seconds, flipping once. Drain on a paper towel-lined sheet pan.
Place the chopped chocolate in a bowl. Boil the cream and pour it over the chocolate and let sit, whisking to combine. Keep warm. Dip doughnuts in chocolate glaze when cooled.