In a large bowl, mix the flour, yeast, salt, and sugar well. Then mix in the egg and the oil and add the water gradually, working it in with your hand—enough to make a soft dough that holds together in a ball. Add more water if necessary, or more flour if it is too sticky.

Turn the dough out and knead on a floured board for 10–15 minutes, until it is very smooth and elastic. Grease the dough all over by putting a drop of oil in the bowl and rolling the dough around in it. Cover the bowl with plastic wrap and leave to rise in a warm place for 1½ hours, or until doubled in bulk.

Punch the dough down and knead again briefly. An easy way of shaping the bagels into rings is to roll out the dough to a rectangle about 1 inch (2½ cm) thick, and cut it into 11 equal strips with a pointed knife. Roll each strip between your palms into a rope about 7 inches (18 cm) long and ½ inch (1½ cm) thick and bring the ends together, pinching them to seal and form a bracelet. Place the rings on an oiled surface, and let them rise for about I hour, or until doubled in bulk

Bring plenty of water to a boil in a wide pan, then lower the heat to medium. Slip in 4 bagels at a time. Boil them for 1–2 minutes, turning them over once as they rise to the top. Then lift them out quickly with a slotted spoon and place them on a cloth to dry. Do the same with the rest of the bagels. Arrange on oiled baking sheets, brush with egg white, and bake in a preheated 375°F (190°C) oven for 15–20 minutes, until nicely browned.

Variations:

Sprinkle the bagels lightly with poppy or sesame seeds, fried onion, or coarse salt before baking.

Another way of shaping the bread is to roll it into small balls, make a hole in the middle, and widen it by pulling the ring from the center.

If you want to make the bagels in the old way, without the egg, you will simply need to add a little more warm water to bind the flour.