Peel potatoes and boil until tender. Drain and reserve potato water. Mash potatoes.
Cream butter and sugar until well blended. Beat in the eggs one at a time, beating well after each addition.
Dissolve yeast in ½ cup of the potato water and add with the mashed potatoes to first mixture. Beat well. Add salt, milk and half of the flour. Beat until smooth. Add enough more flour, a little at a time, to make a stiff dough. Cover and let stand in a warm place until doubled in bulk.
Place on a floured board and divide dough in half. Knead well. Shape into 2 loaves and put into greased bread pans (9×5×3). Cover with a towel and let rise for about 1 hour in a warm place until the loaves are nicely rounded.
Bake 50 minutes in a preheated 375º oven. As soon as you take the pans out of the oven, brush the tops of the loaves with melted butter.