Resoring music to iPod that has been restored to factory settings

iTunes has been reporting that my iPod Classic is corrupted and that I need to restore it, which I've done.

The music (virtually all of it ripped from CDs, not downloads) has been wiped of course.

Because the iTunes library on my Mac is huge, I keep only a portion of it on my iPod. Is there any way to now return that same selection of music to the iPod?

(I have a Time Machine backup running, if that helps).