Begin by heating the milk and butter until the butter begins to melt.
Combine the milk and butter mixture with the yeast and brown sugar in the bowl of a stand mixer.
Add in the salt and 2 cups of flour, beating for 3 minutes.
Knead the dough on a floured surface until smooth, typically about 8 minutes.
Place it in a greased bowl and cover for 1 hour.
Preheat the oven to 400°F.
Warm up the boiling solution until it gets to a rolling boil.
Punch the dough down and divide into 4 equal pieces.
Roll these into balls to make the rolls.
Place each roll in the solution for 2 minutes turning after 1 minute.
Remove the rolls with a slotted spoon and place on a greased baking sheet.
Continue this process for remaining rolls.
Beat the eggs and mix with the water to create the egg solution.
Cut a cross top in each roll.
Brush the egg wash or drizzle it onto each roll.
Bake for 15 minutes, then reduce to 350°F for an additional 12 minutes, until evenly browned.
Let cool, then slice and build sandwiches.