Hello Coopermad,
Thanks for using Apple discussions.
When booted from a recovery volume, you should run Disk Utility beforehand to verify and attempt to repair the drive in question – though there is a good chance you have already tried that and that is when you discovered the EFI problem to begin with. If that’s the case, all you need to do is reinstall Mac OS (or MacOS) as usual and it should be fixed in the process:
Assuming you choose to simply reinstall Mac OS X and you don’t attempt to format the drive or do anything else, then only the Mac OS system software will be replaced and the EFI partition will be recreated in the process. In other words, no personal data, files, or apps should be lost in the process if all you are choosing to do is reinstall Mac OS X. If you go a route aside from simply reinstalling Mac OS X, you may lose data.
Finally, something else to keep in mind is that sometimes damaged or broken EFI partitions can be an indicator of an impending disk failure, or some other problem with the hard drive. If you suspect that may be the case, you may want to attempt to repair the drive through Disk Utility and run Apple Hardware Test on the Mac to see if any hardware related disk errors appear. If the drive is failing, you will need to replace it, and you’d want to do that sooner than later to avoid data loss.