Stir together yeast, 1 teaspoon sugar, and 1/3 cup warm water in a 1-cup glass measuring cup; let mixture stand 5 minutes.
Heat milk, shortening, remaining sugar, and salt in a small saucepan over medium heat. (Do not boil.)
Place mashed potato in a large mixing bowl. Pour hot milk mixture over potato, and let cool. Beat in eggs at medium speed with an electric mixer. Add yeast mixture. Gradually add flour, stirring until a soft dough forms.
Turn dough out onto a well-floured surface, and knead until smooth and elastic (about 5 minutes). Place in a well-greased bowl, turning to grease top. Cover and chill 8 hours.
Roll dough to 1/4-inch thickness on a floured surface, and cut with a floured 1 1/2-inch round cutter, adding flour as needed.
Brush rolls with melted butter; make a crease across each roll with a knife, and fold in half. Place in lightly greased cakepan. Cover and let rise in a warm place (85°), free from drafts, 2 hours or until doubled in bulk.
Bake at 375° for 15 to 18 minutes or until lightly browned.