Weigh and combine the all-purpose flour, water and yeast in a bowl for your quick starter. Stir to make sure there are no dry spots in the starter.
Let starter rest in a covered bowl on the counter for 45 minutes
In your mixing bowl or another large bowl, add the all-purpose flour, yeast, salt and sugar and stir to combine. The goal here is to ensure there are no lumps in the flour.
To your bowl with all your dry ingredients, add your water, all of your quick starter, vegetable oil, eggs and one egg yolk. If you're using a stand mixer, mix with your dough hook for a minute and then knead with the mixer for 8 to 10 minutes. If you're doing this all by hand, you will probably need to knead for 15 to 20 minutes to get a workable dough. By the time you're done kneading you should have a slightly sticky but still very smooth dough.
Add your dough to a slightly oiled bowl and let rise in a warm spot in your kitchen for 1.5 to 2 hours.
Braiding: If you want to try a four-strand braid technique like I typically use, I have a short braiding tutorial with photos in my Monte Cristo blog post. You could use a simpler three-strand braid or try something more complicated like a six-strand braid. For anything other than four strands, you can find tutorials or videos with a google search.
I weigh my entire dough and divide it by four, splitting and weighing each of the four pieces and rolling those into long 18-inch or so dough strands. Then I follow the technique described in the blog link above.
Once your dough is braided, combine your leftover egg white with 1 tablespoon of water in a small bowl to create your egg white glaze.
Paint the braided loaf with half of the egg white sugar wash.
Allow your dough to rise another hour, covered with plastic wrap in a warm spot in your kitchen.
After an hour, pre-heat your oven to 375 degrees F (190 C).
While the oven pre-heats, paint the top of your loaf with the second half of the egg white sugar wash.
At this point after the egg wash has been applied, you can add sesame seeds or poppy seeds. The egg wash helps the seeds stick.
Cook loaf for 35 minutes. Rotate half-way for even browning.
Once done, remove challah from the oven and move to a baking rack to cool. Allow to cool fully before slicing.