Pour water into mixing bowl of electric mixer. Cover with yeast and about ½ tsp. of the sugar. Stir gently to hydrate the yeast. Let it sit for 5-10 minutes to get foamy. (If using instant yeast, skip this step and mix your yeast and water in with everything else in the next step.)
Add the yolks, oil, honey, sugar, flour and vital wheat gluten. With the paddle or dough hook attachment, knead the mixture for about 1-2 minutes, just until all the ingredients are combined. Cover with plastic wrap and allow to rest for 30 minutes.
With the mixer on low (with either the paddle or dough hook attachment), slowly add the salt. Knead for an additional 1-2 minutes until the salt is fully absorbed. Cover with plastic wrap and allow to rest 15 minutes.
Make four folds: Using a bowl scraper, reach under the dough from the bottom center and pull it over itself to the top center. Rotate the bowl 90° and do a second fold. Rotate the bowl 90° and do a third fold. Rotate the bowl 90° and do a final fold. Cover with plastic wrap and allow to rest 15 minutes.
Perform another set of four folds. Cover with plastic wrap and allow to rest for 1 to 1½ hours, until the dough has doubled in size.
Preheat oven to 350° F.
Fold the dough over itself to gently deflate it. If making one challah, divide into three equal portions for braiding. If making two challahs, divide into 6 equal portions. Shape each portion into a ball.
One ball at a time, pat down the ball into a flat oval. Fold the top third of the oval over itself to the center and then again to the bottom. Using the palms of your hands, roll the dough out to a rope approximately 8-10 inches long. Repeat with remaining balls. Braid challah as desired.
Cover loosely with plastic wrap and let rise 30-45 minutes, until the challah is puffy and the dough holds an indentation when you press your finger into the dough.
Apply egg wash. Bake 30-35 minutes.