In large bowl, combine 1-1/2 cups flour and yeast. Mix water, 3 tablespoons sugar and salt together, and add to the dry ingredients. Beat with a mixer for half a minute at a low speed, scraping the sides of the bowl clean. Beat at a higher speed for 3 minutes. Then, by hand, mix in enough flour to make a moderately stiff dough.
Turn out onto a lightly floured surface and knead until smooth and elastic (8-10 minutes). Cover, let rest for 15 minutes.
Cut into 12 portions, shape into smooth balls. Poke a hole in the center with your finger, and gently enlarge the hole while working the bagel into a uniform shape. Cover, let rise 20 minutes.
Meanwhile, start a gallon of water boiling. Put 1 tablespoon of sugar in it, mix it around a bit. Reduce to simmering.
When the bagels are ready, put 4 or 5 bagels into the water, and cook 7 minutes, turning once. Drain them. Place on a greased baking sheet, and bake at 375 degrees F (190 degrees C) for 30 to 35 minutes. Remove from oven, eat hot or cold.
Broiling option: For a glossier surface, place raised bagels on an ungreased baking sheet prior to boiling them. Broil them five inches from heat for 1 to 1-1/2 minutes on each side. Then put them into the hot water to be boiled as above. Note: do not bake broiled bagels as long as non-broiled ones, 25 minutes should be long enough.