To make your sourdough challah, first prepare the starter, in a medium jar or container, combine ½ cup water with ½ cup whole-wheat flour and mix well. Cover and let sit at room temperature for 2 days. Dump out about 75% of it, leaving about a few tablespoons in the jar or container. Feed the starter by adding ½ cup water and another ½ cup whole-wheat flour and mix well. Let sit for another 2 days. Repeat this process every 2 days for 2 weeks total. I like to feed the starter 12 hours before I use it to make bread. After 2 weeks you can keep the starter in the fridge and do the dumping and feeding of it every week. After you feed it, let it sit out at room temperature for a few hours before you return it to the fridge.
To make the preferment for your dough, in a mixing bowl, place the 1 cup warm water, 1 cup of bread flour and ¼ cup of the starter and mix well. Cover with plastic wrap and let sit for at least 12 hours. I usually let it sit for about 14 hours.
In a separate bowl place the sugar, salt and oil. Add the boiling water and whisk well. Add the cold water and mix again. Beat the eggs in a small bowl and add to the bowl of sugar, salt, oil and water, reserving one tablespoon to brush on the loaves before baking. Whisk well. Add 3 cups of bread flour, one at a time, and mix well each time. Add the preferment mixture and mix well. Add another cup of flour and mix in. At this point I dump the dough onto the counter and mix with my hands. Add ½ cup flour and mix. If still sticky, add another ¼ cup flour and mix until the dough is mostly smooth, and you don’t see any flour not mixed in. There is no need to knead, just mix in the flour. It will not be as smooth as regular challah dough. Cover the bowl with plastic.
Place the remaining beaten egg into a small bowl and store covered in the fridge.
After ½ hour, uncover the bowl. Fill a measuring cup with about 1 cup of water, dip your hand into the water and place your fingers underneath one part of the dough, about 3 inches under the dough. Use your hand to lift up that part of the dough and fold it into the center. Turn the bowl and place your hand underneath the next part of the dough and fold over another section. Continue until you have made your way all around the dough, wetting your hand every other fold.
Recover the bowl and let the dough sit for another half hour. Repeat the folding process and let sit for another ½ hour. Repeat the folding process and let sit for another ½ hour and then repeat one more time.
Recover the dough with fresh plastic wrap and let it sit and rise for 10 to 12 hours. It should grow at least 50% bigger, if not more. Sprinkle some bread flour on your counter. Use a plastic bench scraper to scrape the dough out of the bowl onto the counter on top of the flour. Let sit for 10 minutes.
Divide the dough into two pieces. Rub some flour on your palms and fingers and lift one piece of dough above the counter and let it stretch briefly back toward the counter. Place the dough back on the counter and fold the piece you are holding 2/3 of the way over the rest of the dough. Lift the opposite side and fold over to cover the dough, like you are folding a letter.
Give the dough a ¼ turn – so that the seam is now vertical. Grab the bottom of the dough and lift up above the counter briefly, as you did the first time, and let it stretch back down toward the counter. Place the dough back on the counter and fold the piece you are holding 2/3 of the way over the rest of the dough. Take the opposite side and fold over to cover the dough.
Divide each piece of dough into three or the number of strands you want to braid.
Dust your hands with flour again and loosely braid the loaves. Place onto a lined cookie sheet. Let rise for 2 hours.
Preheat oven to 350°F. Add 1 teaspoon water to the reserved egg and mix well. Brush the top of the loaves and sprinkle with any desired seeds. Bake for 35 minutes, or until browned.