That's slate. Very sure. It's a common building material (especially roofing) where it can look and act like that.
Shale is similar. I have a lot of shale deposits nearby, and I can say that stripping paint with a paintbrush would likely break little bits off of it. It's way to fragile to do anything with it. It would be exceedingly difficult to cut it to that shape and keep it that way, as well.