Originally Posted by
miamijim
The opposite side is most likely metal, unscrew that side first, probably left hand thread and then switch sides to remove the remove the plastic cup.
Good eye there, noticing now that the pictured cup appears to be a left-side cup (the ones with a flange that doesn't quite bottom against the bb shell but simply reinforces the spline).
The cup with broken-off flange that I mentioned before was actually a Shimano UN71 drive-side cup, made of alloy.
Luckily, enough of the spline remained allowing it to be turned.