Mix: In a large bowl, combine water, sea salt, 2 eggs, oil, and sugar. Whisk until well beaten and sugar and salt are dissolved. Mix in bread flour. Use a spoon, dough scraper, or your hands. Mix until all ingredients are combined and there is no dry flour left.
Knead: Transfer the dough to an unfloured clean work surface. Measure 200 grams of the sourdough levain and add it to the dough. Knead the levain into the dough mixture for 10 to 15 minutes or until the levain is fully incorporated. The dough should be smooth and release easily from the work surface.
Bulk fermentation: Clean the mixing bowl with warm water to create a warm environment for the dough, or use a different dough container. Put dough in the bowl, cover, and let ferment 3 to 5 hours until the dough is smooth and doubled in volume.
Prepare baking dish: Line 2 baking sheets with parchment paper.
Divide: Divide dough into two 450g (or about 1 lb.) portions for the 2 loaves. Divide again. There will be 4 portions of dough.
Preshape: Lightly flour work surface, roll out a portion of dough into a flat long skinny rectangle. To make a long roll, roll up a long side into a spiral. Repeat with remaining 3 portions of dough.
Braiding: Take two ropes of the dough and cross them over each other into an “X” shape. Take the upper two sections of the ropes of dough and pull down toward the bottom so all four ends are pointed downward. Take four small pieces of paper and label each one with a number: 1, 2, 3, 4. Put the pieces of paper below the ropes of dough, from left to right. As you follow the braiding steps, move each number to align with the rope’s new position. To start: Bring1 over 2, 3 over 4, 4 over 1, 2 over 4, 1 over 3, 3 over 2, 4 over 3, and 1under 2. Tuck all the strands under and seal them against the loaf. The goal of the braiding is to have an alternating and even pattern that comes up higher in the center of the loaf. Hold the ends of the loaf and stretch it if needed to help make the shape more even.
Proof: Cover with plastic wrap, loosely to allow room to expand. Proof for 4-6 hours, until tripled in size (check readiness by lightly pressing dough with finger, if dough springs back wait longer, if indentation stays, it’s ready). A warm environment, protected from drafts is optimal.
Preheat oven: 20 minutes before baking, preheat oven to 350˚, put baking stone (if you do not have a baking stone, bake straight on the baking sheet) in the oven to preheat on middle rack, place rimmed pan with water on lower rack.
Egg wash: Meanwhile, whisk 1 egg with 1 t. water and brush onto loaves for the glaze. Sprinkle loaves with sesame or poppy seeds, if desired.
Baking: Carefully transfer loaves to heated baking stone with parchment underneath. Bake 25 minutes, then remove pan of water, close oven, and bake about 10 minutes longer, until browned.
Cool: Put challah on a cooling rack to cool for 20-40 minutes.