In a large bowl, combine 2 cups flour, sugar, yeast and salt. In a small saucepan, heat water and butter to 120°-130°. Add to dry ingredients; beat until smooth. Stir in mashed potatoes and enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Cover and let rest for 10 minutes. Divide into 16 pieces. Shape each into a ball. Place in two greased 8- or 9-in. cast-iron skillets or round baking pans. Cover and let rise in a warm place until doubled, about 30 minutes.
Preheat oven to 400°. Sprinkle tops of rolls with additional flour. Bake until golden brown, 18-22 minutes. Remove from pans to wire racks.