I just used the phrase "narrow wall", and it occurred to me that, even though my meaning was clear, the word "narrow" usually refers to width and not to depth. Are there words like "tall" and "short" for height and "wide" and "narrow" for width that describe the extent of depth specifically? I'm aware of "shallow" and "deep", but, at least in my mind, those apply only to a different sense of the word "depth".
I think you're looking for thick and thin. In fact, the Oxford Dictionaries uses your exact example for one of its sample sentences:
With opposite sides or surfaces that are far or relatively far apart.
‘thick slices of bread’
‘thick metal cables’
‘the walls are 5 feet thick’
With opposite surfaces or sides that are close or relatively close together.
‘thin slices of bread’
‘a thin line of paint’