It really depends on why the PEEK broke. If it broke because the back of the ferrule is locked into the threads, the best solution is to try and first pull the tubing out using one of those very small round tapered files found in the jewellers file sets you can purchase at most hardware stores.
You could also heat the file as suggested above, but I've found the best way is to screw it in anticlockwise and gently pull. Some of those files have both right and left hand knurling to produce the file surface.
Once the tubing is out ( and if you're very lucky the ferrule as well ), you can use an Easy Out, left hand threaded screw ( not common ) or a sligtly larger tapered round jewellers file ( my preferred choice ), again turning anticlockise to screw it in and then force the ferrule out. If you have to pull the ferrule straight out, ensure you clean the threads before putting a new nut/ferrule in. Patience and care will triumph.
The prevention is to switch to one-piece fingertight ferrules, as sold by Upchurch and others. I use them all the time, even on SS, and they work well for me. Two piece ferrules are supposed to be cheaper, but a 1/16 smooth SS tube pushed through the centre ( or even the center ) will make the one-piece reusable. YMMV.
Bruce Hamilton