Prepare the stiff starter: Mix together the stiff starter ingredients in a small bowl or container. Cover and leave at room temperature for 10 to 16 hours until it is doubled in volume and is full of airy carbon dioxide.
Scald the milk: Pour in more milk than needed to account for evaporation--330g of whole milk. Heat the milk over medium to medium-high heat until it is steaming and proteins begin to stick to the pot. Temperature will be 130 to 140 degrees F. Don't let it foam. Pour into a heat safe carafe to cool to 90 to 100 degrees F.
Make the tangzhong: Whisk together the water and white flour for the tangzhong in a medium mixing bowl. Once the flour is nearly all absorbed, whisk in the milk. Use a spatula to add the mixture to medium sized pot. Heat over medium to medium-high heat, stirring frequently until it changes in form to a starchy mashed potato looking mixture. Transfer the cooked tangzhong back to the mixing bowl and spread out to cool down more quickly, to cool down below 110 degrees F.
Begin mixing the dough: Once the milk and tangzhong have cooled down to the proper temperature, add 300g of whole milk to a very large mixing bowl. Then, add the water, 250-250g stiff starter, all of the tangzhong, sugar, salt, whole wheat flour, and bread flour. Mix until the ingredients are partially combined and a rough dough is beginning to form*
Add eggs: Add the eggs and continue mixing until all the ingredients are well incorporated.
Knead the dough: Knead the dough until it is no longer sticking to the sides of the bowl and pulls away easily from your hands or work surface.
Add the softened butter: Knead in the soft unsalted butter one tablespoon at a time. Continue kneading until all the butter has full incorporated into the dough and the dough is no longer sticky and pulls away easily from your hands or work surface.
Bulk ferment: Place the dough into a greased large bowl or 6-qt. Cambro container, well covered with plastic wrap or a lid. Leave at room temperature for 4 to 6 hours until the dough has doubled in volume.
Prepare loaf pans: Grease two loaf pans with butter or oil or line with parchment paper cut to size.
Divide dough. Divide the dough into six equal pieces (about 324g each section).
Preshape: Form each section into equally shaped round balls.
Shape: Lightly flour the work surface and rolling pin, roll out the first round of dough to 7.5" x 9' rectangular shape. Along the longest (9-inch) edges, fold in the sides of the dough two inches into the center so that they overlap*. This overlap should be about 3 inches wide. Roll up from the long bottom of the dough to create a spiral shape. Pinch where the end of the dough ends to seal the spiraled dough. Set aside.
Repeat: Repeat the shaping process with the other rounds of dough. Once there are three spiral-shaped portions, arrange in one of the loaf pans. Place the last three in the second loaf pan.
Proof: Cover the loaf pans with plastic wrap and proof at room temperature for 1.5 to 3 hours until they have risen and expanded to 1.5 to 2 times their volume.
Preheat: Preheat the oven to 400 degrees F with a heat-safe (metal or cast iron) pan filled with 1-2 inches of water on the lowest rack.
Egg wash: Whisk egg wash ingredients. Use a pastry brush to brush the egg wash over the tops of the unbaked loaves until they are fully covered.
Bake: Place both pans of dough into the preheated steamy oven. Bake 35 to 40 minutes until the tops are golden brown.
Cool: After the loaves have cooled for 5 minutes in the pans, remove from pans and cool on a cooling rack for 20 to 30 minutes.*