In a medium bowl, whisk together the flour, sugar, salt and yeast. In a large bowl, whisk together the water, vegetable oil and egg yolks.

Stir the dry ingredients into the wet ingredients until a shaggy dough forms, 1-2 minutes. Then, transfer to a lightly floured work surface and knead until smooth, 8 to 10 minutes. The dough can be slightly tacky, but not sticky. If the dough is sticky, lightly sprinkle 1 tablespoon of flour at a time and continue kneading until the dough is no longer sticky.

Transfer to a lightly greased bowl and cover with a damp towel. Let sit in a warm area until doubled in size, about 1 hour.

Divide the dough into 8 equal-sized balls. Place on a lightly floured work surface and cover with a damp towel. Let sit for 30 minutes.

Preheat the oven to 350º and line 2 baking sheets with parchment paper. Roll each ball of dough into a 12-inch rope, about 1 1/2 inches thick.

Take 4 ropes of dough and arrange in a lattice to look like a hashtag, with each rope going over and under one another. Take the ends of 2 non-parallel, adjacent ropes and cross them to place the lower rope over the higher rope. Repeat this process all around the challah, then tuck the ends underneath.

Place the challah on a baking sheet and brush with some of the egg white, then garnish with half of the sesame seeds. Repeat this process to make a second challah. Let both rise until the dough is proofed (it doesn't spring back immediately when touched), 30 minutes.

Bake until the challahs are golden brown, 30 to 35 minutes. Remove from the oven and let cool completely before serving.