In the bowl of a stand mixer, combine the dry ingredients.
490 g bread flour, 70 g sugar, 10 g instant dry yeast, 6 g salt
Add the cooled tangzhong along with the remaining wet ingredients to the dry ingredients.
1 whole egg + 1 egg yolk, 150 g whole milk, All the tangzhong
Using your stand mixer fitted with the dough hook, knead the dough for 10-15 minutes.
After kneading, add the softened butter, one cube at a time, allowing each piece to incorporate before adding the next. If the butter is hard to mix in or the dough starts to spin around the hook without mixing, pause the mixer, scrape down the bowl and dough hook, and restart.
115 g unsalted butter
Continue kneading for 10-15 minutes, until the dough is smooth, elastic, and passes the windowpane test (when a small piece of dough can be stretched thin enough to let light through without tearing).