Place cubed potato and enough water to cover in small saucepan. Bring to a boil; reduce heat to medium-low. Cook potatountil fork-tender. Drain, reserving 1/2 cup of the potato water. Mash potato to measure 1/2 cup; set aside.
In the same saucepan combine potato water, 1/4 cup of water and1/2 cup butter. Heat until very warm (120 to 130 degrees F).
Meanwhile, in a large bowl, combine 2 cups of the flour, the sugar,salt, and yeast; mix well. Add warm potato water mixture; beat until well blended. Add remaining flour, 1/2 cup at a time, beatinguntil smooth. Cover and refrigerate 8 to 24 hours.
Grease cookie sheets. Punch down dough several times to remove all air bubbles. Place dough on lightly floured surface. Knead dough 6 to 10 minutes or until smooth and elastic. Dividedough into 16 pieces. Shape each into smooth, round bun; place on greased cookie sheets. Cover loosely with plastic wrap and cloth towel. Let rise in warm place (80 to 85 degrees F) until doubled in size, about 45 minutes.
Heat oven to 375 degrees F. Uncover dough. Cut 1/4 cup cold butter into 16 equal pieces. Press one piece into the center of each bun. Sprinkle each with 1/2 teaspoon sugar. Bake 20 to 30 minutes or until golden brown. Serve warm.