Boil the potato until tender. Rice or mash. Stir milk and yeast together until yeast is dissolved in the bowl of a stand mixer. Add the sugar, warm potato, salt, butter, egg, flour, and yeast mixture and, using a dough hook, mix until a smooth, slightly sticky dough forms. Place dough in a large, buttered bowl and cover with a tea towel.
Allow to rise in a warm spot for about 45 minutes or until doubled in bulk.
Butter a 9x13 inch baking pan and punch the dough into the pan. Cover and allow to rise, about 45 minutes. Preheat oven to 375. In a small bowl, use a fork, your hands, or a pastry cutter to cut the cold butter into the sugar and cinnamon for the topping until it looks sort of like wet sand.
Press shallow dimples in the dough, sprinkle with sugar mixture in an even layer over the cake.
Bake 20 minutes or until the topping is bubbly and browned. Cool in pan for 20 minutes prior to serving.