Place water, flour, 2 tablespoons sugar, salt, and yeast into a bread machine in the order listed, or follow the order recommended by the manufacturer if different. Run 'Dough' cycle. Remove dough from the machine after the cycle is done, about 90 minutes.

Place dough onto a lightly floured surface and let rest for 10 to 15 minutes.

Cut dough into nine equal pieces. Roll each piece into a small ball and flatten into a circle. Poke a hole in the middle of each circle with your thumb. Poke your thumb through the hole and twirl each circle a bit to enlarge the hole and to even out dough around the hole. Place back onto the floured surface, cover with a clean cloth, and let rest for 10 minutes.

While dough is resting, bring 3 quarts water to a boil in a large pot. Preheat the oven to 375 degrees F (190 degrees C). Sprinkle cornmeal onto an ungreased baking sheet.

Stir 3 tablespoons sugar into boiling water. Working in batches, carefully transfer two bagels at a time to the boiling water and boil for 1 minute, turning halfway through. Drain briefly on a clean towel, then arrange on the prepared baking sheet. Brush with egg white and sprinkle with poppy seeds.