Prepare the Starter: Feed your sourdough starter a 50:50 bread to water ratio. Cover and set in a warm place to allow it to double in size and activate. This typically takes 3-6 hours.
Once the starter is active and bubbly, weigh out 175g of starter and put into the bowl of your stand mixer.
Prepare the Dough: Next, in a small saucepan heat the milk and sugar on low until brought to around 100 degrees. Stir until the sugar is dissolved.
Add the sweetened milk and eggs to the sourdough starter and mix on low speed with your dough hook until combined.
Slowly begin adding in flour, 1/2 cup at a time. Continue to mix on low/medium speed. Once roughly mixed, cover and allow to rest for 30 minutes to autolyze.
After autolyze, add salt and begin mixing on low/medium speed. As the dough is kneading, begin adding in cubed butter pieces.
Continue kneading until the dough is smooth, silky, and passes the windowpane test; which typically takes 10 minutes of total kneading.
Transfer the dough to a large bowl and cover. Allow this to be proved overnight. Because of the high fat content of the dough, I prefer to keep it from ever getting overly warm. So proof at room temperature rather than in a warm proofer.
Baking Day
After the overnight bulk fermentation, your dough should have risen and doubled. Now it's ready to be shaped.
Divide Dough: Dump the dough onto a floured work surface and divide into three equal pieces.
Shape the Dough: Then begin working each individual piece into a 12-14" long coil by rolling on the worksurface. Do this for all three pieces of dough.
Next, you will braid the three coils. Once braided, tuck the ends under the braid and carefully place into a parchment lined loaf pan. Cover with plastic wrap and let the dough rise for 1 hour at room temperature.
Prepare to Bake: Preheat the oven to 375 degrees.
In a small bowl whisk together one egg and 1 Tbsp. of water, using a pastry brush gently brush the egg over the loaf.
Place the bread into your preheated oven for 35-40 minutes. The internal temperature of the bread should reach 180 degrees.
Notes
If the top of your bread is getting too brown during baking, cover with a piece of aluminum foil for the remainder of its baking time.