Hi Tom,
As you have realised, restoring an entire Windchill instance to recover a single item is probably not worth the effort.
The process to restore a single or a few items, should go like this:
What you need to be able to do is translate from Windchill name to the underlying name of vault filename - this is usually a hexadecimal number and you can see all these files in the Windchill Vault filesystem.
It would then be possible to find the file in the filesystem of your Windchill Vault as they don't get deleted at the filesystem level even if deleted in Windchill, unless you perform a "remove un-referenced files" using the vault admin tool.
Even if you have performed a "remove un-referenced files", if you back up your file system to tape the file/files can be restored from tape.
You can then rename these files to be able to be opened in the authoring application and save them back into Windchill as new items.
Unfortunately - for you to be able to do all of this you need to be able to know what the underlying filename was in the vault filesystem - ie the hex number, and I suspect that you don't know this. I don't think that there is a way for you to do this retrospectively - if anyone else wants to chime in and explain, please enlighten me...
So in future, what would be wise would be for you to ask PTC or your VAR if there is a script that you can run against your Windchill System every night before you run your backup to dump all the windchill partnames to filesystem name relations from the database so that you can do this in future. The process is known as listvaultfiles
I have a script that does this, but unfortunately I cannot share it with you as it is not mine to share :-(
If you were really desperate and these files were super important, you could restore the Windchill DB from backup to a different schema name in Oracle from a time when the item was in the system and then search this for the Windchill Part name to Vault Filename conversion so you could just restore the vault file, but again it probably is not worth the effort.
I appreciate it probably is not the answer you want, but maybe this will help you understand the process it a bit better and set you up for the future.
Rgds
Gary