In a liquid measuring cup, combine the warm water, milk, yeast, and sugar. Let stand until foamy, about 5 minutes. Meanwhile, use a whisk to beat 2 eggs in a small bowl.
In a large bowl, whisk the flour with the salt. Add the butter to the flour and gently rub it in with your fingers. Stir in the yeast mixture and beaten eggs with a wooden spoon until the dough starts to come together.
Dump the dough onto a well-floured counter and knead vigorously, folding the dough onto itself and throwing it down onto the counter. Work with it for about 10 minutes, adding additional flour when the dough gets sticky. Shape the dough into a ball and return it to its bowl. Cover with plastic wrap and let the dough rise in a warm place until doubled in bulk, about 2 hours.
Line a baking sheet with parchment paper. Using your knife, divide the dough into 8 equal parts. Gently roll each part into a ball and arrange 2 to 3 inches apart on a baking sheet. Cover loosely with a clean dish towel and let the buns rise in a warm place for 1 to 2 hours.
Preheat the oven to 400 degrees F with the rack in the center. Fill a metal pan with water and set it on the oven floor or bottom rack (see Note).
In a small bowl, beat the remaining egg with 1 tablespoon of water and brush some of the mixture on top of the buns with the pastry brush. If you are using seeds and/or coarse salt, sprinkle them over the egg wash. Place the buns in the oven and bake, turning the sheet halfway through baking, until the tops are golden brown, about 20 minutes. Transfer to a rack to cool completely.
Room temperature: covered container or sealed bag, 2 days
Freezer: cut in half lengthwise, freezer bag, 6 months
NotesCook's Note: I don't care if you only have a glass pan, do not use it for this purpose! If the pan stays filled with hot water throughout, the glass will be okay. But if (hypothetically) the water evaporates and you go to refill it, and if (not quite thinking straight) you pour cold water in your hot glass pan (I know, I know! You can already see how this is going to end), the pan will not so hypothetically explode, propelling shards of glass through your kitchen and at your children, who will then refuse to put on shoes while you cry and pick glass out of your hamburger rolls. Just use the metal pan.
Reprinted with permission from The Homemade Pantry by Alana Chernila, Clarkson Potter copyright (c) 2012