In a small saucepan, heat milk, water, and butter to 120 degrees.
In a large bowl, mix 2 cups flour, yeast, charcoal powder, sugar, and salt. Add the warm milk mixture to flour and then stir in the egg and mix until a sticky dough forms.
Stir in remaining flour, and mix until its pulled together into a shaggy dough. Turn out onto floured surface and knead until smooth and elastic, about 8 minutes.
Divide dough into 12 equal pieces. I used a kitchen scale to weigh out my dough in order to get the same sized buns. Roll into smooth balls and place on a parchment lined baking sheet and gently flatten a bit.
Cover hamburger buns and let rise for 30-35 minutes. Brush egg wash over tops of buns and sprinkle black sesame seeds.
Preheat oven to 400 degrees and bake for 10-12 minutes. Cool completely before slicing.