Cook potatoes in boiling salted water until tender. Drain them completely, reserving 1/2 cup of the potato water; cool the potato water to lukewarm. Mash the potatoes and measure out 1 cup for making the rolls. Cool to room temp. Or...prepare the same amount using reconstituted instant potato flakes. Dissolve the sugar in the lukewarm potato water and sprinkle the yeast over the surface. Let the yeast mixture stand until it becomes foamy, about five minutes; then stir to dissolve. Combine the butter, milk and salt in saucepan and heat until the butter is just melted. Remove from heat and use a wooden spoon to mix in the 1 cup of reserved mashed potatoes; add in the lightly beaten egg, then the dissolved yeast. Transfer dough to the bowl of a mixer fitted with a dough hook. Slowly add in 4 cups flour, one cup at a time. Knead on low speed until the dough is smooth and elastic, four to five minutes. Then cover the bowl with a clean tea towel and set it in a draft-free place until it has doubled in size, about one hour. Punch down. Knead in the remaining 1/2 cup flour, as needed. The dough should be soft and slightly sticky, but firm enough to just hold its shape. Cover bowl and allow it to rise in a draft-free place for another 30 minutes. Place the dough on a clean cutting board that has been dusted with a little flour and divide into two dozen equal pieces. Dust each piece with a little more flour and roll into a ball. Place the balls about 1-inch apart on a well-greased baking sheet. Cover the pan with a clean tea towel and let the rolls rise for another 15 to 20 minutes (or for about 40 minutes if the dough was refrigerated). Use a pastry brush to lightly brush the tops of the rolls with a little milk, then bake them in a 400-degree F oven for 10 to 12 minutes. Makes two dozen rolls.