Making chinese bbq pork buns

Okay. For years. I have not been able to replicate how the hell my mother made these completely delicious pork buns. I've looked up recipes online, I've experimented, I keep winding up with passable, but not great buns.

I called her today and finally asked.

Okay. For context. The usual recipe is this:

Warm water 1 cup
Active dry yeast 1 (1/4-ounce) package
Flour 1 cup
Sugar 1/4 cup
Shortening or oil 2 T
Water 1/2 cup
Salt 1 1/2 teaspoons
Flour 3 to 3 1/2 cups


Right?

My mother, instead of oil or water - uses butter and milk. And adds an egg.

My mother has been putting bbq pork into steamed brioche for years.

Pictures and recipe to follow. I have some weirdass mashup of French Quarter Redneck pulled pork bbq buns going on here.