Whisk together the warm water, milk, yeast and sugar; set aside. Beat the egg in a separate bowl.
Add the flours, salt, and butter to the bowl of a stand mixer. Using the paddle attachment, mix the ingredients until the butter is the size of pebbles.
Add the yeast mixture and the beaten egg. Run the mixer on medium-low speed until a dough forms, about 5-8 minutes.
Scrape down the sides of the bowl if necessary, and shape the dough into a ball. It will be sticky. Cover bowl with plastic wrap or a very damp kitchen towel, and let the dough rise until it has doubled in size, about 1-3 hours @ 70 F.
Line a baking sheet with parchment paper. Using a floured dough scraper (or chef’s knife), divide the dough into 8 equal pieces.
To shape the dough into balls, gently flatten each piece like a pancake. Gather the ends and pinch the dough to seal in the center. Flip the dough over, cup the surface with your palm, and roll into a ball. Transfer to your baking sheet, placing them a few inches apart. Cover and rest for 1-2 hours, or until puffy and slightly risen.
To make the egg wash, beat the egg with a splash of water. When the buns are finished with the 2nd rise, gently brush each one with egg wash. Optionally, add sesame seeds to the top of your rolls.
Preheat your oven to 400 F. and place a skillet or metal baking dish on the oven floor. Before the dough goes in, add about ½ cup of water to the pan to create steam. Bake for about 15-20 minutes or until golden brown. Transfer to a wire rack to cool completely.
