Add the flour, sugar, salt and yeast in a bowl of a stand mixer and use the paddle on the lowest speed to incorporate all the ingredients.
In a separate bowl, whisk the egg yolks and vegetable oil until blended. Add the warm water while whisking.
Add the egg yolk mixture to the dry ingredients and mix on low speed for about 10 seconds. Let the mixture sit for one minute so that the flour becomes hydrated. After the minute has passed, mix the dough until it is mostly hydrated and looks like a messy dough.
Switch to the dough hook and knead the dough on low speed for 5–7 minutes. The best way to tell if the dough is ready is by pulling off a little piece and stretching it between your fingers. If you pull it gently and it breaks immediately, it isn’t ready.
Remove the dough and gently form it into a ball. Place the dough in a large bowl, cover with a thin layer of oil and cover with plastic wrap.
Allow the dough to rest and rise for 8–10 hours—overnight is perfect!
Turn the dough out onto a lightly floured surface. Divide the dough into two equal pieces. Divide each half into as many pieces as you would like and roll them into long strands for braiding.
Braid the strands into your desired shape (I prefer a four-strand braid). Place the loaves onto a cookie sheet lined with parchment paper and let rise for 4-5 hours.
Brush the dough with the egg whites, making sure to get into the crevices of the braid. Sprinkle on seeds, if you so desire. Bake at 350°F for 30 minutes or until the center registers at 190°F with an instant read thermometer. Remove and let cool on a cooling rack.
