Ikea. Hanging rail. Or a French cleat created on regular cabinets. Plus plenty of scribe molding.

Exactly: IKEA cabinets would be perfect for your application (if you haven't selected cabinets already).

We had a similar issue come up with a kitchen we redid about ten years ago. The house was built of hollow clay block, which was sort of a precursor to concrete block. As we considered how to handle it, we realized that not only did we need to hang cabinets (this was pre-IKEA in our area, and installers were doing the cabinets, anyway, so weren't prone to thinking outside the box), we also needed to add wiring and lighting. What to do?

We built a false 2x4 wall right against the hollow clay tile exterior wall. Yes, we lost 4" of floor space, and yes we had to modify the trim on two windows. But we could safely run wiring, and install the needed outlets and boxes for wall lights.

If you used 2x2's for furring - you could then mount 2x4's horizontally on the wall - and use them as bridging.

I'd use construction adhesive, and counter sink blue screws to attach the 2x4's.

Then you can mount the cabinets using regular screws into the 2x4's.