Dissolve the yeast. Place the water in a small bowl, sprinkle with the yeast and a healthy pinch of sugar, and stir to combine. Let stand until you see a thin frothy layer across the top, 5 to 10 minutes. This means that the yeast is active and ready to use. (If you do not see this or if your yeast won't dissolve, it has likely expired and you'll need to purchase new yeast.)

Mix the dry ingredients. Place 4 cups of the flour, sugar, and salt in the bowl of a stand mixer and whisk to combine. (Alternatively, use a large bowl and knead by hand.)

Add the eggs, yolk, and oil. Make a well in the center of the flour and add the eggs, egg yolk, and oil. Whisk to form a slurry, pulling in a little flour from the sides of the bowl.

Mix to form a shaggy dough. Pour the yeast mixture over the egg slurry. Mix the yeast, eggs, and flour with a wooden spoon or rubber spatula until a shaggy dough that is difficult to mix forms.

Knead the dough for 6 to 8 minutes. Fit the mixer with the hook attachment and knead on low speed for 6 to 8 minutes. (Alternatively, turn out the dough onto a floured work surface and knead by hand for about 10 minutes.) If the dough seems very sticky, add flour a teaspoon at a time until it feels tacky, but no longer like bubblegum. The dough has finished kneading when it is soft, smooth, and holds a ball-shape.

Let the dough rise until doubled. Place the dough in an oiled bowl, cover with plastic wrap, and place somewhere warm. Let the dough rise until doubled in bulk, 1 1/2 to 2 hours.

Divide the dough and roll into ropes. Divide the dough into 3 or 6 equal pieces, depending on the type of braid you'd like to do. Roll each piece of dough into a long rope about 16 inches long. If the ropes shrink as you try to roll them, let them rest for 5 minutes to relax the gluten and then try again.

Braid the dough. Gather the ropes and squeeze them together at the very top. If making a 3-stranded challah, braid the ropes together like braiding hair or yarn and squeeze the other ends together when complete. If making a 6-stranded challah, the directions are below.

Let the challah rise. Line a baking sheet with parchment paper. Place the braided loaf on top and sprinkle with a little flour. Cover with a clean kitchen towel. Let rise in a warm place away from drafts until puffed and pillowy, about 1 hour.

Brush the challah with egg white. About 20 minutes before baking, arrange a rack in the middle of the oven and heat to 350°F. When ready to bake, whisk the reserved egg white with 1 tablespoon of water and brush it all over the challah. Be sure to get in the cracks and down the sides of the loaf.

Bake the challah 30 to 35 minutes. Bake, rotating the baking sheet halfway through, until the challah is deeply browned and registers 190°F in the very middle with an instant-read thermometer, 30 to 35 minutes total.

Cool the challah. Let the challah cool on a cooling rack until just barely warm. Slice and eat.