Scrub potato; prick several times with a fork. Place in a medium saucepan; add water to cover. Bring to a boil; reduce heat, and simmer 20 to 30 minutes or until tender. Drain potato, reserving 3/4 cup water. Let potato cool slightly. Peel and mash potato, reserving 2/3 cup. Reserve remaining potato for another use.
Cool reserved 3/4 cup water to 105° to 115°. Combine water, yeast, and brown sugar in a 1-cup liquid measuring cup; let stand 5 minutes. Combine yeast mixture, 1 1/2 cups flour, dry milk, and salt in a large mixing bowl; beat at medium speed of an electric mixer until well blended. Add potato, egg, and oil, beating well. Gradually stir in enough of remaining 1 1/4 cups flour to make a soft dough.
Sprinkle 2 tablespoons flour evenly over work surface. Turn dough out onto floured surface, and knead until smooth and elastic (about 5 minutes). Place in a bowl coated with cooking spray,turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in bulk.
Punch dough down, and divide into 24 equal portions. Shape each portion into a ball, and place balls on a baking sheet coated with cooking spray.
Cover and let rise in a warm place, free from drafts, 30 minutes or until doubled in bulk. Bake at 400° for 10 minutes or untilgolden.