Combine the starter, water, and flour for the levain in the bowl of a stand mixer and mix until the flour is fully incorporated. Cover the bowl with plastic wrap and leave to ferment at room temperature for 8 to 12 hours.

Once the levain is ready, add the warm water, egg yolks, honey, oil, and bread flour to the bowl. Knead the mixture using a stand mixer on medium speed for about 5 minutes. Gradually incorporate the salt and continue kneading for another 3 minutes until the dough becomes elastic and can pass the windowpane test. Transfer the dough to a large, ungreased bowl, cover with plastic wrap, and let it rise at room temperature for 4 to 6 hours.

Divide the dough into three equal parts for a single large braid, or two equal halves for two smaller loaves. Each section should be divided further into the desired number of strands. Roll each piece into long ropes and braid accordingly. Cover loosely with plastic wrap and let rise at room temperature for 5 hours. The dough should appear puffed and increased in volume, not doubled. Press gently with a finger—if the indentation springs back slightly, it’s ready to bake; if it returns quickly, bake immediately to avoid over-proofing.

Toward the end of the final rise, preheat the oven to 350°F. Brush the challah with egg wash and apply any preferred toppings.

Bake for 30 to 35 minutes until deeply golden on both top and sides.