It doesn't take much of a musical detective to see (and hear) the Countess's famous aria, "Porgi, amor" from The Marriage of Figaro in the melody - it's even in the same key:
Now it would take more of a musicological detective than I feel like being to unearth the history of this J.C. Bach piece. As far as I can tell, it's a resetting of a recit/aria by the great Giuseppe Gazzaniga, of whom I know nothing - here one can hear a sampling of Gazzaniga's "Mi scordo a torti miei...Dolci aurette" sung by a self-billed modern Farinelli (!), but that sample doesn't include the recit intro above which is the only place where Mozart's famous tune shows up. (When I was growing up dreaming of being a great baseball player, it never would have occurred to me I'd type that last sentence.) Anyway, it's well-established that JCB was a big influence on WAM, so it's not at all unlikely that this admittedly simple melodic idea could have passed from one to the next.
I'm sure anyone who's run across this Gazzaniga/J.C. Bach concoction will have noticed this connection, but my extensive web-based research didn't come up with anything, so let me be the first to make this Gazzaniga grift Googleable. If nothing else, I'm almost certainly the first to type that last sentence.
TOMORROW (or soon): More Recent Tune Theft Discoveries!