I think I found it.
(I would have paid $10 if they had cleaned off the cobwebs and Daddy Long Leg carcasses for me.)
I primed it with a gray primer and then lightly sprayed with Krylon Brushed Metallic paint in Satin Nickel. It has a little bit of sheen to it, but not too much.
I'm certainly not done with the mantel, but this big shutter is a start.