How do I install a butcher block breakfast bar on a half wall?
I have a similar bar/half wall situation, but with a granite top instead of butcher block. In my case, I screwed a piece of MDF to the top of the half wall, and the countertop installers then glued the granite to that with a strong adhesive. This works because the granite is doubled at the edges, so the MDF is mostly hidden. If it would be feasible for you to rout the bottom of the butcher block 1/2" deep everywhere except the edges (I'd suggest leaving an inch around the edges full thickness), then you could do pretty much the same thing as me, with a layer of MDF screwed to the wall to provide support for the butcher block.

Make sure that the MDF is installed level - otherwise, when you level the butcher block, you'll have MDF peeking out from under it at one end. Don't ask me how I know...