Add the yeast to 1/4 cup of the milk and stir in the sugar. Let sit until the yeast begins to foam
Add the salt and then half of the flours, followed by the yeast mixture, half of the milk and half of the water to a stand mixer
with the paddle attachment. Mix until a paste forms, and then add the remaining flours, 1 cup at a time, and the remaining milk and water until the dough begins to come together. Remove the paddle and switch to a dough hook, and then knead
for 4 minutes.
Form the dough into a ball and then transfer to a lightly-oiled bowl, spinning the bowl around the to make sure the dough is well coated. Cover with a tea
towel and allow the dough
to double in size, about 2 hours.
down the dough and form into 16 equal-size balls. Form the balls into 16 equal-size dowels and place side by side on a parchment-lined baking sheet, nearly touching. Allow the dough to double in size once again.
Preheat the oven to 350 degrees F.
Mix the egg with 1/4 teaspoon water in a bowl and brush each bun with egg wash
. Bake until golden brown and fully cooked through, 20 minutes.
Let cool completely before serving, about 1 hour.