Add both whole wheat flour, bread flour and starter for levain and set aside for 6 hours.
The Tangzhong (Flour-Water Roux):
In a medium saucepan whisk together lightly the flour, water and milk in a saucepan until smooth and there are no lumps. Place the saucepan on the stove, and over medium heat, let the roux cook till it starts thickening. Keep stirring/ whisking constantly so no lumps form and the roux is smooth.
If you have a thermometer, cook the roux/ tangzhong till it reaches 65C (150F) and take it off the heat. If you do not have a thermometer, then watch the roux/ tangzhong until you start seeing “lines” forming in the roux/ tangzhong as you whisk/ stir it. Take the pan off the heat at this point.
Let the roux/ tangzhong cool completely and rest for about 2 to 3 hours at least. If not using immediately, transfer the roux to a bowl and cover using plastic wrap. It can be stored in the refrigerator until the color changes . Discard the tangzhong after that.
In a bowl of kitchenaid stand mixer add bread flour, salt, sugar, and milk powder and set aside.
In a microwave safe bowl heat milk, whipping cream and butter for about 30 seconds and set aside.
Kitchenaid stand mixer fitted with dough attachment mix in, tangzhong mixture, milk-cream-butter and starter into flour mixture and knead until it become soft and sticky for about 15 minutes on medium speed (3-4) . Once the dough starts leaves the side and knead with hand for about 3 more minutes or until when you pull the dough it will spread without tearing, means it passes window pan test.
Remove the dough and place it into well oil pan bowl for doubling. Cover with plastic wrap and a towel, and let the dough rise for about 12 hours or till almost double in volume in room temperature.
Place the dough on your working surface. About 823g dough divide into 4 equal pieces of 206g. You do not need flour to work or shape this dough.
Roll out each portion of the dough with a rolling pin into an oval shape, about 1/8” thick. Take one end of the dough from the shorter side of the oval and fold it to the middle of the oval. Take the other end and fold so it slightly overlaps the other fold.
Roll this folded dough with the rolling pin so the unfolded edges are stretched out to form a rectangle. Roll the rectangle from one short edge to the other, pinching the edges to seal well. Do this with each of the four larger pieces and place them, sealed edges down, in a well-buttered loaf tin. Cover with a towel and leave the dough to rise for about 2-4 hours.
Carefully brush the tops of the dough with egg wash and bake at 350F for about 45 minutes or it registers an internal temperature of 190-200 F. If the top starts browning earlier, tent the loaf tin with foil to prevent extra burning. Let them cool in the tins for about 5 minutes and then unmold and transfer to a rack till slightly warm or cool.