Combine 1 1/2 cups flour and yeast in a large bowl. Mix water, 3 tablespoons sugar, and salt together; add to dry ingredients. Beat with a mixer for half a minute at low speed, scraping the sides of the bowl clean. Beat at a higher speed for 3 minutes. Then mix in enough flour by hand to make a moderately stiff dough.
Turn out onto a lightly floured surface and knead until smooth and elastic, 8 to 10 minutes. Cover and let rest for 15 minutes.
Cut into 12 portions and 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 and let rise for 20 minutes.
Meanwhile, start a gallon of water boiling. Add in remaining 1 tablespoon sugar and mix it around a bit. Reduce to simmering.
Preheat the oven to 375 degrees F (190 degrees C).
When bagels have risen, put 4 or 5 bagels into the water and cook for 7 minutes, turning once. Drain.
Place drained bagels on a greased baking sheet and bake in the preheated oven for 30 to 35 minutes. Remove from the oven and eat hot or cold.
Broiling option:
For a glossier surface, place raised bagels on an ungreased baking sheet prior to boiling them. Broil them, 5 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.
