In a small bowl, dissolve sugar in warm milk. Sprinkle the yeast over the milk mixture and let it stand until frothy, about 5 minutes.
In a large bowl, combine mashed potatoes, melted butter, and salt.
Stir in the yeast mixture and gradually add flour until a soft dough forms.
Knead the dough on a floured surface until smooth, about 6-8 minutes. Place in a greased bowl, cover, and let rise until doubled, about 1 hour.
Punch down the dough and divide into 12 portions. Shape each portion into a ball and place on a greased baking sheet. Cover and let rise until doubled, about 30 minutes.
Preheat oven to 375°F (190°C). Bake rolls until golden brown, about 15-20 minutes.
Allow to cool slightly on a wire rack before serving.