Put potato into boiling water and boil for 15 minutes. Discard potato and let water cool to about 110 degrees F.
Transfer 1/3 cup of the potato water to a small bowl. Sprinkle yeast over top of water and stir to combine. Set aside for 3 minutes.
Sift flour, salt, and 1/2 tablespoon of the sugar together into a large bowl. Add yeast mixture. Stir in another 2/3 cup of the potato water and the oil. Add eggs one at a time and stir briskly until a dough ball is formed.
Turn dough out onto a floured surface and knead for about ten minutes until dough ball is firm, adding a little extra flour if needed. Place in a greased bowl, turning the dough so all sides are greased. Cover the bowl with a clean towel and set aside in a warm place for about 1 hour until dough has risen to double its original size. Punch the risen dough down to flatten and remove from bowl.
Cut dough into 18 equal pieces and shape each piece into a 6- to 7-inch-long, 3/4-inch-thick rope. Bring the ends of one rope together and pinch closed. (A little water on the ends will help secure them.) Repeat until 18 rings are formed. Cover all rings with the towel and let rise for 20 minutes.
Preheat oven to 450 degrees F. Lightly grease a cookie sheet and dust with cornmeal.
Bring the 2 quarts water to a boil. Add the remaining tablespoon of sugar to the boiling water. Drop the bagels into the water one at a time, cooking each for 3 minutes, turning once.
As each bagel is removed from the water, place it on the cookie sheet.
If desired, paint the tops of the bagels with 1 egg white that has been beaten with 1 teaspoon water.
Bake for 12 to 15 minutes, until golden brown.