How to Make It
Place potato in a medium saucepan; cover with water. Bring to a boil. Reduce heat; simmer 15 minutes or until tender. Drain in a colander over a bowl, reserving 1 cup cooking liquid. Mash potatoes with a fork.
Cool reserved cooking liquid to 105° to 115°. Stir in 1 teaspoon sugar and yeast. Let stand 5 minutes.
Lightly spoon 4 1/4 cups flour into dry measuring cups; level with a knife. Combine mashed potato, yeast mixture, 1 tablespoon sugar, 4 cups flour, butter, salt, and egg in a large bowl, stirring until well blended.
Turn dough out onto a floured surface. Knead until smooth and elastic (about 10 minutes); add up to 1/4 cup flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel tacky).
Place dough in a large 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 size. (Press two fingers into dough. If indentation remains, the dough has risen enough.) Punch dough down; cover and let rest 10 minutes.
Divide dough in half; divide each half into 12 equal portions. Working with 1 portion at a time (cover remaining dough to keep from drying), shape portion into a 2-inch-long oval on a floured surface. Roll up tightly, starting with a long edge, pressing firmly to eliminate air pockets; pinch seam and ends to seal. Place roll, seam side down, on a baking sheet coated with cooking spray.
Repeat procedure with remaining dough portions, placing 12 rolls on each of 2 baking sheets. Sift 2 tablespoons flour over rolls to lightly coat. Cover rolls and let rise 45 minutes or until doubled in size.
Preheat oven to 350°.
Bake at 350° for 10 minutes with 1 baking sheet on the bottom rack and 1 baking sheet on the second rack from the top. Rotate baking sheets; bake an additional 10 minutes or until rolls are browned on bottom, lightly browned on top, and sound hollow when tapped. Remove from pan; cool on wire racks.