What could be behind this?
 

Our house is a 1929 tudor in south Minneapolis, above the mantle was a mirror that we just removed, the mirror was dated on the back 1960. This backing is heavy duty cardboard. What could be underneath this?

A chimney!

Looks like old style sheet rock to me or someone just installed it backwards.
What the plans for that area?

It looks more like MDF. Like a faux panels to hide stone behind it or some old brick. Not to sound silly but have you tried to look behind it ?!

Drywall that was never painted but this kind of drywall only came available in the fifties so it wasn't there when the house was built
So tyhis may be hiding a very nice brickwork chimney or perhaps the chimney was added later and nothing back there but ugly.
As suggested it should be opened for peek see.