Mixing and storing the dough: Whisk together the flour, yeast, salt, and vital wheat gluten in a 5-quart bowl or a lidded (not airtight) food storage container.
Combine the liquid ingredients and mix them with the dry ingredients without kneading, using a spoon, a 14-cup food processor or a heavy duty stand mixer with paddle.
The dough will be loose, but will firm up when chilled. Don't try to use it without chilling for at least 2 hours. You may notice lumps in the dough but they will be gone in the finished product.
Cover (not airtight) and allow the dough to rest at room temperature until it rises and collapses, approximately 2 hours.
Refrigerate it for at least 2 hours before using. The dough can be stored and used over the next 5 days, or store the dough in the freezer for up to two weeks in an airtight container. Freeze it in 2 lb portions. When using frozen dough, thaw it in the refrigerator for 24 hours before use, then allow the usual rest/rise times.
On baking day, grease a non-stick brioche mold or an 8 1/2 x 4 1/2-inch nonstick loaf pan. Dust the surface of the refrigerated dough with flour and cut off a 2-pound (cantaloupe-size) piece of dough (you can make a one-pounder as well). Dust the piece with more flour and quickly shape it into a ball. Place the ball into the prepared pan and allow to rest, loosely covered with plastic wrap, for about 1 hour 45 minutes. (dough should no longer feel cold and will have a bit of spring to it).
Thirty minutes before baking time, preheat the oven to 350 degrees F, with a rack in the middle of the oven where your baking stone should sit. If not using a baking stone, a 5-minute preheat should be enough.
Just before baking, use a pastry brush to paint the loaf’s top with egg wash.
Bake the loaf near the center of the oven for about 40-45 minutes. For smaller or larger loaves you will need to adjust the resting and baking times–a one-pounder should need only about 35 to 40 minutes in the oven.
Remove the brioche from the pan and allow it to cool on a rack before slicing. If it refuses to come out of the pan, allow to rest in hot pan for 10 minutes and it should unstick to the sides and slide out.