In your mixer's bowl, add the milk and sugar and stir until the sugar dissolves. Then, add in the yeast and carefully mix it together. Cover this and let it sit for 15 minutes to bloom the yeast.
½ Cup Milk, 2¼ Tsp Active Dry Yeast, ¼ Cup Sugar
Add the yu-dane/tangzhong/roux, milk powder, egg, flour, and salt to the yeast mixture, and stir this with a rubber spatula until it's roughly mixed and a dough starts to form.
2 Tbsp Dry Milk Powder, 1 Egg, 2⅔ Cups Bread Flour, 1 Tsp Salt
Using your mixer's dough hook, start to work the dough on medium for about five minutes.
Once the dough has kneaded for a while, start adding the butter one tbsp at a time, mixing for at least 30 seconds in between each pat. Scrape the sides of the bowl down when all the butter is added and incorporated.
4 Tbsp Butter
Continue kneading, bumping up the mixer speed. On my Kitchenaid, I had it at around 7 for this part. You want to knead for at least 5-10 more minutes, scraping the bowl down as necessary.
Once the dough can be pulled from the bowl cleanly, transfer it to a lightly floured surface and form it into a ball. Put it in a clean mixing bowl and cover with plastic wrap or a towel, and let it rise for 1-2 hours or until it's doubled in size.
After this rise, grease your loaf pan with butter and a light coat of flour. Set this aside.
Drop the dough onto your floured surface again, and divide it into 4 equal parts. Roll each part into 6" squares and fold in the corners and roll almost like a cinnamon roll, then seal the edges with a pinch.
Places these seam-side down in the loaf pan next to one another, then cover and let rise again, once more until doubled in size.
Preheat your oven to 350℉. When preheated and ready to go, brush the top of your bread with either an egg wash or some milk, then bake for 30 minutes. If it seems like it's browning too much at around 25 minutes, tent some foil over it.
Remove from the oven, let cool, and enjoy!