Restoring Time Machine backup to bootable external USB

[brianus]

I have a TM backup of a Mac mini server. The server itself is currently away for repair (its internal boot hard drive died), but I want to restore the TM backup to an external USB HDD that will be bootable so that I can use it as the server's main drive as soon as I get it back. Is it possible for me to do the restore on another Mac? I really just want to transfer the contents of the TM backup, verbatim, to this new USB HDD, so that it will act as a bootable replica of the old server drive.

All of the guides I've found online mention booting to the OS X Install disc, but it would be a huge inconvenience, not to mention it doesn't seem like it should be necessary, to do so. I need to *use* my desktop (non server) Mac while I'm doing the restore; I cannot have it offline for hours while it's doing nothing more than copying files from one external drive to another. Isn't there any easy way to do this?