Peel and cook the potatoes for about 30 minutes or until tender, drain them and save the water.
Grease a large bowl and set it aside. Grease a cookie sheet and set it aside.
Mash the hot potatoes. Add salt, sugar, and 3 tablespoons of melted butter and beat well. Add 1-½ cups of the potato water and milk, stir to blend, and set aside to cool until lukewarm. Add the yeast and stir in 4 cups of flour, beating well. Add enough of the remaining flour to make a stiff dough. Knead the dough on a floured surface until smooth and elastic. Place in the greased bowl, turning to grease all sides. Brush the top with melted butter. Cover and let rise in a warm place until it has doubled in size (this may take several hours). Place on a floured surface and pat out to a thickness of about ½-inch; do not knead again. Pinch off small pieces and shape into small rolls. Place on the prepared cookie sheet and let rise until more than doubled in size. Bake at 400 degrees F for 20 minutes, or until lightly browned.