Add butter, water and milk to saucepan. Heat until butter is melted; set aside and cool to 110°-115°F.
Place the mashed potatoes and potato-water mixture in a large bowl. Add the sugar, salt and eggs. Beat with a wooden spoon until smooth. Stir in yeast.
Add the 5 cups of flour, 1 cup at a time, stirring with the wooden spoon until the dough is smooth and only slightly sticky. Gradually add the remaining flour, working it with your hands by pressing flour into dough and turning dough over until it is smooth and only slightly sticky.
Place dough in oiled bowl; cover and let rise until doubled in size, about 1 hour. (See note below for overnight option)
Punch dough down and place on a floured surface. Press dough out with fingers to a square about 1-inch thick. Cut in 1 1/2 -inch wide strips lengthwise and equal width crosswise. If the knife gets sticky while cutting, just dust it with flour.
Shape each piece into a ball by pinching all four sides underneath to seal. Round on counter to smoot out top. Place buns almost touching in greased 9x13-inch pans or 1/4 sheet pans. Cover; let rise covered until indentation remains after touching, about 30 minutes.
Preheat oven to 400°F.
Bake for 15-20 minutes until golden. Remove from oven and brush with melted butter. Serve warm or at room temperature. Store in an airtight container at room temperature for several days.