Feed your starter about 12 hours before you plan to make this recipe. This gives it plenty of time to get nice and active.
Combine all of the ingredients in the bowl of a stand mixer. Knead on medium speed until the dough becomes smooth and glossy. This will take about 10–15 minutes. The dough is very wet at first—resist the urge to add more flour. It will come together with time.
Cover bowl with plastic wrap, beeswax wrap, or a tight-fitting lid. Let it rise in a warm spot for about 8 hours, or until doubled in size.
Place the risen dough in the refrigerator for at least a few hours (or overnight). Chilling makes the sticky dough much easier to handle when it’s time to shape.
Prepare your pan by either greasing well, or lining with parchment paper. Turn the chilled dough onto a clean surface and divide into two equal portions (a bench scraper works great for this). Cut each half into eight pieces, giving you a total of 16. Shape each into a ball.
Use 8 pieces of dough in each bread pan. Place each dough ball into each parchment-lined loaf pan. Cover and let rise again until doubled—this will take 6–8 hours, or you can leave it overnight.
Preheat the oven to 425°F. Make the egg wash by whisking together the egg and water. Brush the top of the dough in each pan.
Bake loaves for 15 minutes, then loosely cover with foil to prevent over-browning.
Continue baking another 10 minutes, until the brioche is golden brown and baked through (about 25 minutes total). Allow to cool in the pan for about 5 minutes and then remove to finishing cooling on a wire rack.