A Tattered Note
 

Is it possible to get another one of these without having to recreate a new character?

I don't think so

If you're an Iksar, you can get the newbie note reward back. I don't think any other race would even need their newbie note, as there are no other races with newbie item quests (that I know of).

http://wiki.project1999.com/The_Penance

I sure would not spend much time trying to get one. Not like you get 4 levels of XP and a CoF. :p