In a small bowl or measuring cup, stir together the water, milk, sugar and yeast. Let it stand for about 5 minutes, until it's foamy. (If it doesn't foam, the yeast is kaput - get some fresh yeast and try again!) Crack the egg into it and beat it a little with a fork to break it up.
Meanwhile stir together the flour and salt; add the butter and blend it in with a pastry blender, whisk or your fingers, rubbing it until it's crumbly, as if you were making pastry. Add the yeast mixture and stir until you have a soft dough; beat it with a dough hook in your stand mixer or knead it on a lightly floured countertop until it's nice and smooth; 5-10 minutes. It will be stickier than regular dough; resist the urge to add too much flour. Leave it tacky.
Place the ball of dough back into the bowl, cover it with a tea towel and let it sit for an hour or so, until doubled.
Divide the dough into 8-10 pieces (or 20 if you want wee slider buns), shape them into balls, place them a couple inches apart on a baking sheet that has been sprayed with nonstick spray or lined with parchment or a silicone mat, cover loosely with plastic wrap and let rise for another hour.
Preheat the oven to 400ºF. Brush the buns with a little beaten egg if you like, and sprinkle them with sesame seeds.
Bake for 10-15 minutes (a bit longer if you made larger buns) until golden.