No bread machine versions, just the original and authentic versions: Place the water in a large bowl. Sprinkle the yeast over. Add the first measure of sugar. Beat the egg. Let stand until foamy (about 10 minutes). Add the egg to the yeast mixture. Stir in 75% of the flour. Add the first measure of salt. Stir rapidly using a fork until the flour is just moistened. Knead until the dough forms a ball. Let rest for 15 minutes. Lightly oil a large bowl. Set aside. Turn the dough out onto a lightly floured surface. Knead, adding only as much of the remaining flour as needed to keep the dough from sticking, until it is smooth and elastic (about 8 minutes). Shape the dough into a ball. Place in the oiled bowl, turning to bring the oiled side up. Cover and let rise in a warm place away from drafts until it doubles in size (about 30 minutes). Divide the dough equally into pieces, one per finished bagel. Shape each into a ball. Flatten each ball in the palm of your hand. Poke a hole in the center with your finger. Stretch the dough to make the hole about 1" in diameter. Lightly moisten a baking sheet with water. Place the bagels on the baking sheet. Cover with a cloth and let rise until doubled (50-60 minutes). Preheat the oven to 475 degrees. Bring water to a boil in a medium skillet or kettle. Add the second measures of sugar and salt to the water. Boil each bagel in the water for 1 minute per side. Place a linen towel on the baking sheet. Transfer the bagels to the towel on the baking sheet. Bake 5 minutes. Remove from the oven. Turn the bagels over onto an ungreased baking sheet (without a towel). Bake until golden brown and the bagels make a hollow sound when gently tapped (20-25 minutes). Serve warm or at room temp.