In a mixing bowl, combine 1 1/2 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 1/2 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 1/2 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. Put bagels in water and begin timing when they rise to the top. Cook about 3 to 4 bagels at a time for about 3 minutes, turning once. Drain. Place on greased baking sheet. Bake at 375° for 25 to 30 minutes. Makes about 1 dozen bagels.