The correct term is doppio tostato, "double roasted". Some of the earliest Italian refrence material, roasting logs etc. make quite a mention of this process as do alot of the early Dutch manuals. Some equate this process to better stabilization of the bean which supposedly equates to a longer freshness due to all sorts of blah, blah, blah.
I think it's a dark and dirty little "old world" secret that no one wants you to hear about.
One of my close friends who has been under illy's employ for the last 15 years turned me onto that one.