Whisk all the dry ingredients (bread flour, wheat flour, sugar, salt, yeast) in the bowl of the stand mixer or the food processor.
Add the milk, egg and the Tangzhong. Mix until they all come together and form dough.
Now add the butter and continue to knead on medium high speed until the dough become smooth and elastic. This takes about 15 to 20 mins. To test of the dough has reached the right consistency I used the thin membrane technique. Take a small piece of dough in your hands and stretch it slowly on all 4 sides. If the dough forms a membrane without breaking apart, then you know that the dough has kneaded enough. If the dough breaks into pieces when trying to stretch, knead it for few more minutes and try again.
Placed the dough in a well oiled bowl and wrap it with plastic. Let it rise in a warm spot until doubled in volume. The original recipe said about 40 mins, but it took me about 1 ½ hrs to double in volume.
On a lightly floured surface deflate the dough and divide into 3 equal parts. Being in a fancy mood, I weighed my three parts and made sure they were of equal weight. Make balls out of the 3 parts and rest it again for about 15 minutes covered with plastic.
After resting (for the dough and you), roll each part into long oval.
Now fold the dough vertically over each other and then flip the dough over with the seam side under.
Now roll it again vertically into a long oval piece about 12 inches long.
Starting from the end farthest from you start making a tight roll into a cylinder shape and place it in greased loaf pan seam side down. Repeat this step for the rest of the 2 balls of dough and place them next to one another in the loaf pan.
Leave this to proof for the second time, wrapped with plastic, until it rises ¾th of the height of the pan. This took about 45 minutes for me.
Brush the loaf with egg wash or milk and bake in a preheated 350 F oven for about 30 -40 mins. The top has to become nice golden brown and the bread would sound hollow when tapped. If the top browns too quickly, tent the pan with foil during the last few minutes of baking.
Remove the loaf on a cooling rack and let it cool completely before slicing this whole wheat bread.