In a mixing bowl, combine 1 ½ cups of the flour and the yeast. Combine water, the 3 tablespoons sugar, and salt; pour over flour mixture.
Beat at low speed of electric mixer for ½ minute, scraping bowl a few times. Stir in as much flour as you can mix with a spoon.
Turn out onto a lightly floured board and knead in enough flour to make a moderately stiff dough that is smooth and elastic (about 8 minutes).
Cover with a clean towel and let rest 10 minutes.
Cut into 12 equal portions; shape each portion into a smooth ball. Punch a hole in the center of each ball and pull gently to make a 1 ½ inch hole in the center.
Place on a greased baking sheet. Cover and let rise 20 minutes. Broil bagels 5 inches from the heat for 4 minutes, turning once.
Tops shouldn''t brown. Heat 1 gallon of water with 1 tablespoon of sugar; bring to a boil then reduce heat.
Cook about 3 to 4 bagels at a time, turning once. Drain.
Place on greased baking sheet. Bake at 375° for 25 to 30 minutes.Makes about 1 dozen bagels.