For sponge and first rise:

Whisk together warm water, yeast, sugar, oil, eggs and flour. Stir this mixture, which is a very loose dough. Let rise in a warm place until doubled in volume, about 1 hour. Gently deflate the air out of it and add ½ cup sugar, salt and enough of the remaining flour to allow dough to hold together. Turn out onto a lightly floured surface and knead until smooth. Grease large bowl and place dough inside, turning to grease both sides.

Second rise:

Cover bowl with plastic wrap and let rise in warm place for 1 hour, until doubled in size.

Third rise:

Once dough has risen, gently punch down to release air bubbles, then cover and let rise again for another 30 minutes.

Shaping:

To make a 4 braid round challah, take half of the dough and form it into 4 equal balls. With hands, roll each ball into a strand about 12 inches long and about 1 ½ inches in diameter. Place the 4 strands crosswise, two and two, like tic-tac-toe, going over and under. Take an “under” strand and crossover a top strand, repeat 4 times, then go backwards, taking the under strands over the top strands. Tuck in the ends when you run out of rope. Repeat with the other half of the dough to make the second challah. Place braided loaves on parchment paper on high-quality cookie sheet with at least 2 inches between them. Brush beaten egg onto loaves.

Fourth rise:

Let loaves rise in warm place for one hour. Preheat oven to 350°F and brush risen loaves with remaining egg wash, then sprinkle lightly with sesame seeds. Bake in center of oven for 35 to 40 minutes, or until golden (and until they sound hollow when tapped). If desired, to have a more uniform color, remove from oven after 15 minutes and reapply egg wash to the light areas that have appeared as the loaves have risen in the oven. Return to oven to complete baking.