In a medium bowl mix the water, milk and sugar together - add the yeast, then set aside until foamy, about 5 minutes.
In a large bowl, whisk the flour together with the salt. Add the butter, and rub gently with your fingers until the mixture resembles small crumbs.
Use a wooden spoon to mix in the yeast mixture and the beaten egg, stirring until a dough forms.
Turn the dough out onto a well floured surface and knead for about 8 - 10 minutes, or until smooth. (this dough is very sticky, so it's best to knead it by scraping it up and slapping it on the counter repeatedly - be careful to not add too much flour, or you risk making the rolls too tough.)
Form the dough into a ball, return it to the large bowl and cover it with a damp towel. Let it rise in a warm place until doubled in size - 1 to 2 hours.
Line a baking sheet with baking paper and divide the dough into 6 or 8 equal parts. (depending on if you want huge or enormous rolls)
Roll each piece of dough into a ball and space about 3 inches apart on the baking sheet.
Spray some plastic wrap with cooking spray, cover the rolls and let rise again for another hour or two, until doubled again in size.
Preheat the oven to 400 F (200 C) and put a shallow pan full of water on the bottom of the oven.
Beat the egg and water and gently brush over the top of the rolls.
Bake on the center rack for about 15 minutes, turning the baking sheet halfway through baking, until golden brown then remove to a wire rack to cool.