Place potato in a small saucepan; add water to cover. Bring to a boil. Reduce heat; cook, uncovered, until tender, 10-12 minutes. Drain. Transfer to large bowl., Using a stand mixer, beat potato until smooth. Leave only 1/2 cup in bowl (save remaining for another use). Beat in 4 cups sugar until smooth. Gradually add enough remaining sugar until dough forms a ball., Divide dough in half. On a surface dusted with confectioners' sugar, roll half of dough into a 10x7-in. rectangle. Spread 1/4 cup peanut butter to within 1/2 in. of edges. Roll up jell-roll style, starting with a long end. Cover and refrigerate until firm, at least 1 hour. Repeat with remaining dough and peanut butter. Cut into 1/4-in. slices. Store in the refrigerator.