I just found this not too long ago and have been humming it ever since: Mike Patton’s cover of Ennio Morricone’s Deep Deep Down, originally sung by Christy for the Danger:Diabolik soundtrack. Patton’s version really builds upon the original and sounds great live with a full orchestra backing him. There’s is talk of an album of covers of Italian pop songs from the 50s and 60s—which would include Deep Deep Down— but I have yet to find any hard release dates.
I’ve also included a clip of the version by Christy (it’s the English version; for some reason I can’t find the original Italian).
Speaking of great Morricone covers, the always versatile John Zorn (a long-time collaborator of Patton’s) has a brilliant album of Morricone covers that has been out for years called The Big Gundown. Here are two live versions of pieces that are on the album, Erotico and The Battle of Algiers.