Combine water, sugar, salt, bread flower and yeast in bread machine, and run dough program.
When the dough is ready, divide into 8 balls on a lightly floured surface. Make a 1" hole in each ball. Place bagels on a greased baking sheet, cover, and let rise for 30 minutes or until they have doubled in size.
In a pot, bring 8 cups of water to a boil, and add 2 tbsp of sugar. Simmer a few bagels at a time for about 3 minutes, turning to make sure they cook evenly. Return the boiled bagels to the baking sheet.
This part is optional: Beat the egg, and brush a small amount on the bagel tops, sprinkle with sesame seeds, poppy seeds, or cracked wheat, etc.
Bake at 400F for approximately 25 minutes, or until done.