Combine yeast, 1 teaspoon sugar, and water. Let stand 5 minutes or until bubbly.
Combine remaining sugar, potatoes, milk, shortening, eggs, and salt; add to yeast mixture, stirring well. Stir in 2 cups flour. Add enough remaining flour to make a soft dough.
Turn dough out onto a floured surface, and knead 10 minutes or until dough is smooth and elastic. Place dough in a greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Punch dough down; shape into 1 1/2-inch balls. Place balls 1 inch apart on greased baking sheets. Cover and repeat rising procedure 1 hour or until doubled in bulk.
Bake at 400° for 12 minutes or until lightly browned.