I just took down a ceiling fan to find an electrical box that I've never seen before:
It appears to be wrapped around the ceiling beam. The center screw is drilled into the bottom of the beam. Looks like the two slits on either side have holes drilled into the beam, and that's what I would attach a new ceiling light fixture to.
Is this sort of thing ok? I've just never seen it before, not sure what it's called, and it if it's ok for code in New York.