If desired, prepare a proofing oven by turning on the oven light and warming the oven to 300°F for 2 to 3 minutes before turning it off.
In a large bowl, whisk together the bread flour, sugar, yeast, and kosher salt.
Add the warm water, warm milk, and vegetable oil.
Mix until a shaggy dough forms.
Knead by hand for 6 to 8 minutes, or with a stand mixer for 5 to 7 minutes, until smooth and tacky.
Place the dough in a lightly oiled bowl, cover, and let rise for 15 minutes.
Divide the dough into 8 equal portions.
Shape each portion into a ball.
Flatten into a rectangle approximately 4 x 6 inches.
Roll tightly into a log and pinch the seam closed.
Roll gently on the counter until about 6 inches long.
Arrange seam-side down on a parchment-lined baking sheet.
Cover and let rise for 15 minutes, or until puffy and touching.
Whisk together the egg and water and brush over the buns.
Bake at 375°F for 18 to 20 minutes, or until golden brown.
Cool before slicing and serving.