Is there such a thing like low profile/depth electrical box to install a power outlet on a cinder wall that has no framing?
Easy as pie with metal boxes.
The problem is most people tend to go straight for plastic boxes (which kind of ignores the whole reason we have boxes; to ground out loose wires and contain arcing fires).
The standard 4x4 metal box is only 1-1/2&quot; deep.  They also make 1-gang boxes only 1-1/4&quot; deep.   These are the common cheap boxes, not a pricey specialty item.
A 4x4 box, you mount it flush to the studs and then use a &quot;Mud Ring&quot; the thickness of the drywall and the mud ring gives you a 1-gang or 2-gang opening.  With a 1-gang box, you can mount it flush to the drywall, so you're going less than an inch into the insulation.