A section of 'skin' to match the cabinets and applied directly to the back would have been much easier to make match.

About the only thing you can do now is make the section into the wall it appears as and trim it out to match the rest of the room;.

The lack of any hold back from the ends of the cabinet section mean that anything is not going to look nice without a lot of work to camouflage the faces of the 2x4s.

Even a other layer of skin on the end of the cabinet is going to produce a problem at the from of the cabinet.

It does not appears they have much experience with kitchens.

Need to agree with post above,this isn't top quality workmanship...You might be able to "hide" the back of 2x4 wall, with beadboard,but the 2x4 sides are an issue..There doesn't seem to be a way to place a veneer over it,without really screwing up the exisitng side of cabinets,and even if you built out the side of existing cabinet to take a veneer, it would compromise the look of the front,unless you used a piece of cove molding to trim-up the side corner..

Best of luck

I've hired a finishing carpenter to fix this. The board the cabinet company gave me was laminate cherry, not the real thing, as I ordered.

We're trimming out the sides like this, using 4" for the verticle pieces and the shoe:

We're trimming out the seating side like the part of this island behind the sink  the four framed panels:

We'll use half bullnose molding to round to the corners to the kitchen side of the island (like the first pict where the wood meets the yellow shelves). I think it will all work out.