In a small saucepan, whisk together the flour and water until smooth.

Cook over medium heat, stirring constantly for 2 to 5 minutes until it thickens into a paste.

Transfer the pasty tangzhong to a heat-safe container and cool completely before using it in the dough recipe. A tangzhong can be made 1 to 2 days in advance.

In a large bowl or stand mixer bowl, combine the sourdough starter, slightly cooled milk, sugar, eggs, and the cooled tangzhong. Combine these ingredients using clean hands, a hand mixer or the paddle attachment on low speed if you're using a stand mixer.

Add both flour and salt to the bowl and mix until the ingredients are fully combined. The dough should be glossy and stick a bit to the bottom of the bowl. Use a dough hook attachment at medium speed in this step if you are using a stand mixer.

Add in the butter about 2 tablespoons at a time as you mix the dough. Mix until all the butter is fully incorporated.

Cover the bowl with a tight-fitting lid, damp towel, or plastic wrap. Place it in a warm spot or in the fridge to proof and double in size overnight (8-12 hours).

On the next day, transfer the enriched dough to a lightly floured work surface. Using your hands or a bench scraper divide it in half and then into 16 equal portions and roll each part into a ball.

Place 8 balls in each buttered or parchment-lined loaf pan.

Proof the dough for 2-3 hours at room temperature or until it doubles in size or slightly crests the pans edges.

Preheat your oven to 350°F and brush the top of the sourdough brioche dough generously with the egg wash.

Bake the bread until it turns deep golden brown and gets to an internal temperature that’s between 185°F - 200°F . The baking time will be about 30-35 minutes and I recommend keeping an eye on the bread at the 25 minute mark.

Let the enriched bread cool completely on a wire rack before slicing and enjoying!