In a large bowl, mix together the first three ingredients.
Then soften the yeast in a small bowl with 0.25c water.
Dissolve malt extract in 1 cup hot water.
Let malt mixture cool down to warm. Make a well in the center of the flour mixture. Pour into the well, in this order: Softened yeast mixture, malt water.
Stir together until smooth. Beat this dough vigorously to develop the gluten. To make a very stiff dough, gradually add the flour.
Turn out on a floured surface and knead for a full 10 minutes. Divide dough into dozen equal pieces. Shape each piece into a ball. Cover balls of dough with a cloth and work with one at a time. Place the ball on a very lightly floured surface. Flatten slightly. Poke the center of the ball with a forefinger, going all the way through. Now use the fingers of both hands to gently open up the ring. Try to keep the doughnut-shaped roll you are forming symmetrical. The hole should be about one-third of the bagel's diameter. Place shaped rings on a non-stick baking sheet. Cover and let rise for 15 to 20 minutes. They should not quite double in size. Meanwhile, ready the boiling liquid. In a large pot, heat the water.
Stir the malt barley into water.
Heat to boiling. Reduce heat and keep regulated to a healthy simmer. Preheat oven to 250ºC . One at a time, slip risen bagels into simmering water. Bagels should float. If they sink, do not worry. They will soon rise to the surface. After about 30 seconds, turn them over. They should remain in the water about 1 minute in all. You may simmer several at a time, but do not crowd them in the pot. Remove with a skimmer and place one inch apart on a non-stick baking sheet. Brush bagels with a mixture of 1 egg and 1 T water. If desired, sprinkle with coarse salt or poppy seeds.
Bake at 250ºC . for 10 to dozen minutes, or until well-browned. Cool slightly on wire racks. Serve warm.
Note: In place of unbleached white flour, equal parts of stone-ground rye flour, stone-ground whole-wheat flour, and unbleached all-purpose flour may be used.