In the bowl of your stand mixer, combine your tangzhong, the rest of the milk, vital wheat gluten, egg, yeast, sugar, salt, and about half the flour. Mix.

Add more flour, slowly, until a shaggy dough forms. I tend to err on the side of adding less flour than I'll probably need, and add more, slowly, every few minutes as the dough kneads.

Knead the dough for 10-12 minutes (yes, it's a long time--I've found that longer kneading times helps a whole wheat dough develop stronger gluten). Continue kneading until your dough seems stretchy and strong.

Slowly add the room temperature butter in chucks, as the mixer continues kneading. Allow the dough to knead for another 3-5 minutes until the butter is all mixed into the dough, with no chunks remaining. The dough should be soft, workable, and stretchy. At this point, you should be able to achieve a decent windowpane if you've kneaded the dough long enough. (To test for windowpane, pull a chuck of dough off and stretch it between your fingers, as in the picture above. If you can get it thin enough to see some light through without the dough instantly ripping, you're in the right ballpark.)  You don't want the dough too stiff or too soft, but somewhere in the middle. If you're not able to pass the windowpane "test" without the dough ripping, keep kneading longer and try again.

Place the dough in a warm spot in an oiled bowl and let it rest for about 1-1.5 hours. The dough doesn't have to double in size, as long as it rises some.

Gently pull the dough out of the bowl and shape into 12 rolls, and place them evenly in a 9x13 pan.

Set the pan aside to let the rolls rise for another 1-1.5 hours. This time you really want to give them enough time to double, if possible.

Preheat your oven to 350, and bake the rolls for about 20 minutes, until they're cooked through and slightly golden on top. I really try to not overcook them, infact they often look like they're slightly undercooked when I pull them out.

While the rolls are still hot, brush the tops with butter.