Place potato cubes in a small sauce pan and cover with salted water. Bring to a boil, then reduce heat to medium-low and simmer until tender, about 15 minutes. Drain and cool.
Mash potato in a large bowl until smooth.
Stir 1 cup confectioners' sugar into mashed potato; mix well. Gradually stir remaining confectioners' sugar and milk to form a firm dough. Incorporate green food coloring at this point if using.
Sprinkle work surface with confectioners' sugar, and roll dough into an 8x12-inch rectangle about 1/2 inch thick.
Spread peanut butter evenly onto the dough.
Tightly roll dough into a log, jelly roll-style, beginning at the wide end.
Wrap log in plastic wrap and chill in refrigerator until the candy sets up, about 1 hour. Cut into 1/4-inch slices.
