Peel potatoes and boil until tender. Drain and reserve 3/4 c of cooking water. Mash the potatoes and stir in the potato water; set aside. Dissolve yeast in the warm water and add the 1 teaspoons salt.
Add the yeast mixture to the potato mixture; mix on low speed to blend.
Cream the butter and add the 1 c of sugar a little at a time along with the salt and beaten eggs.
Stir in the yeast mix. Mix well and add 3 c of the flour (1 c at a time) beating vigorously after each cup.
Dough should be soft but not wet so add up to 1/2 cup more flour if necessary. Cover bowl and let rise until doubled, about one hour.
Grease a 9x13 pan or two 8" square pans. When dough has doubled, punch down and turn onto floured surface and sprinkle top with flour. Let rest five minutes. Roll to 1/2 to 3/4" thick and as close to the shape of the pan as possible. Place in the pan/pans, cover and let rise until doubled.
Make topping by creaming the butter. Beat in the sugar and flour. Add eggs, one at a time and beat well after each. Add just enough milk to make the mixture easy to spread over the cake; it should not be runny.
After gently spreading the topping on the risen dough, bake in preheated oven at 350 for 35-45 minutes. Let cool in pan.