While you are making your tang zhong, whisk the yeast into the lukewarm milk with a fork and let stand for 10 minutes.
In a stand mixer bowl whisk together the flour, salt, and sugar, then attach the dough hook and add the yeast and milk mixture, plus the water, the tangzhong, and the eggs. Mix for 6 minutes on medium low speed, the mixture will be smooth.
Add the softened butter, a tablespoon at a time, waiting for each tablespoon to incorporate before adding the next. Once the butter has mixed in, continue to mix for 5 minutes.
Remove dough from mixer, shape into a ball and allow to rise in lightly greased bowl for 1.5 hrs or until doubled.
After this resting period, punch down dough, then spread slightly on a lightly floured surface, covered with damp towel, for 10 minutes. Meanwhile, make the glaze (next set of instructions)