Barbutte, Open Sallet, Gjermundbu, Bascinet and there are plenty more that let you expose that glorious beard as well as giving you protection.
But the Nordic Conical, Pronoia, Munitions helmets, Blue Flat Topped helmet I am just not sure about their full face, and rarely see them used compared to the others, bringing the chainmail down to something similar to what they did with the Roman helmets or the Nordic pot I think just looks a lot nicer