One side plasterboard, the other a stud.
I have a multi-tool and can cut away par of the stud. I want to avoid any hard hits with a wood chisel or all the nails in the plasterboard will become evident.
The only way I can think off is to cut a wing off the plaster dry lining back-box somehow, and glue the remains of the side back in place. And to screw the bottom to the stud with a woodscrew.