Add the flour and using a dough hook mix for 4 minutes on low.
3 ¾ Cups All-Purpose Flour
Increase the speed to medium and add the salt, mixing for another 3 minutes.
1 Tablespoon Salt
Finally, add the cold butter, one tablespoon at a time and mix for another minute or two after each addition. Continue to mix until no pieces of butter remain. This is going to be odd to see that butter slapping around in there, but trust me, as you mix, the dough will firm up and be silky and all butter will be incorporated.
3 Tablespoons Unsalted Butter
Place the dough in a lightly oiled (olive oil or vegetable oil is great) bowl, turning over to coat, cover with a towel and allow to rise for 1 to 2 hours.
Place a silpat or parchment paper on a baking sheet and shape the dough into 4-8 hoagies depending on size preference. I like to flatten each piece into a rectangle, fold one end up like an envelope, turn 180 degrees and fold up the other end over the first. Repeat until you've formed a hoagie and pinch shut the seam and end seams.
Place seam side down and repeat with remaining dough.
Cover lightly with a towel and allow to rise another 1 to 2 hours.
Whisk together the egg white and milk. Using a razor blade, make a slit down the top of each roll. Brush each top with the egg mixture.
1 Egg White, 1 Tablespoon Milk
Preheat the oven to 375ºF, place the hoagie rolls on the baking pan and bake for 16 to 22 minutes.
Remove from the oven when they are lightly golden and feel hard when you tap the crust.
Rub with a little butter if desired and allow to cool.
The bread is hard upon removal but quickly softens, so don't worry that you over baked.