Cook potato in boiling water to cover 10 minutes or until tender. Drain, reserving 1 cup liquid; set potato aside.
Heat reserved 1 cup liquid to 100° to 110° in a small saucepan. Sprinkle with yeast; stir and let stand 5 minutes.
Mash potato in a large bowl with a potato masher or fork; stir in yeast mixture, shortening, sugar, and salt. Let stand at room temperature 2 hours. Gradually add 4 cups flour, stirring to make a soft dough. Place dough in a well-greased bowl, turning to grease top. Cover and chill 8 hours.
Punch dough down; turn out onto a surface sprinkled with remaining 1/2 cup flour, and knead 4 or 5 times. Roll to 1/2-inch thickness; cut with a 2 1/2-inch round cutter, and place on lightly greased baking sheets.
Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.