In a large bowl, whisk together the water, yeast, milk, sugar, butter, salt, and egg. Add the flour and stir, with a stout spoon, until the mixture is too stiff to stir.
Turn the dough onto a work surface, and knead it, by hand, until smooth and elastic -- 5-7 minutes.
Wash out, dry, and lightly grease the mixing bowl. Drop the dough into the bowl, and then flip it to grease the other side. Cover the bowl with plastic wrap, and let rise or "proof" until doubled in volume -- 90 minutes to 2 hours.