Cook 1/3 cup flour and 1 cup water in a small saucepan over medium heat, whisking constantly, until a thick paste forms (almost like a roux but looser), about 5 minutes. It's ready when it reaches about 149 degrees F, the temperature when the starches in the flour gelatinize and the tangzhong comes together into a pudding-like roux.
Add milk and honey and cook, whisking to blend, until honey dissolves. Make sure the mixture isn't above 120 degrees F, lest you kill your yeast.
Transfer mixture to the bowl of a stand mixer fitted with a dough hook or a large mixing bowl and add milk powder, yeast, salt, 2 eggs, and 5 remaining cups flour.
Knead on medium speed until dough is smooth, about 5 minutes, or knead by hand for about 10 minutes.
Add butter, a piece at a time, fully incorporating into dough before adding the next piece, until dough is smooth, shiny, and elastic.
Coat a large bowl with nonstick spray and transfer dough to bowl, turning to coat.
When the dough looks like it has doubled in size and is puffy to the touch (if you poke the dough it should hold the indent and slowly fill back in), take the dough and split into 8 equal pieces. Roll each piece into a ball.
Cover with plastic wrap and let rest for 15 minutes.
Grease two 9x5-inch loaf pans and set aside.
Roll one piece out on a lightly floured surface into a long oval. Fold the right third of the oval over the middle, then fold the left third of the oval over the middle to make a long, narrow packet. Lightly roll over the seam to flatten and seal.
Roll the packet up from the bottom to make a fat roll. Repeat with other seven balls of dough.
Arrange four rolls of dough, seam side down, in each prepared loaf pan. Cover with plastic wrap. Let proof for another 40 minutes until the dough reaches just below the rim of the loaf pan.
Preheat oven to 350 degrees F.
Beat remaining egg with 1 teaspoon water in a small bowl to blend. Brush top of dough with egg wash and sprinkle with coarse salt, if desired.
Bake, rotating pan halfway through, until bread is deep golden brown, starting to pull away from the sides of the pan, and is baked through, about 30 minutes.
Let milk bread cool slightly in pan on a wire rack before turning out; let cool completely.