It's a CR8, at least I think that's the shorthand they use on the Les Paul forums - a Gibson custom shop 1958 LP Standard reissue, but with a Chambered body.
I know we often go on about the various types of chambering/weight relief Gibson use on US production Les Pauls, but until a couple of weeks ago I had no idea they made chambered Historics. I don't think they're in regular production, they just do limited runs from time to time.
I haven't looked in the control cavity yet, but as I understand it these have fully-chambered bodies with a solid block around the pickups and bridge area:

It definitely sounds and feels a bit more airy and resonant than a solidbody LP, but it's not like a 335 acoustically since the sides and top are still pretty thick.
Apart from that, it's like any other R8 - long tenon, BIG chunky neck, holly headstock veneer and all that vintage gubbins. I don't know what the colour is called, unfortunately, but I'm trying to find out! :D I don't think it's Iced Tea, it may be Bourbon Burst or even Faded Tobacco Burst but pictures of the different colours are so inconsistent.