I have had to fudge a bit here. Van Morrison's Astral Weeks is probably my favourite, or Let It Bleed, or Get Yer Ya-Ya's Out by The Stones.
They've both featured, so I'll default to my next favourite album: Let It Be
There are innumerable videos for this song out there, including a demo where Paul swears at the beginning that I found once, but never again, and one where some dude has overdubbed the two different guitar solos; but I like this version; under-produced, nice backing "ooo-ooo"s.... though if I'm honest I prefer the original (album) solo. It's... dirtier.
Go, seek, find
Edit: Persistance does pay, it would seem, although my memory isn't what it was apparently. A demo with heavy vocals, bass and swearing, at about 1:54.
So not the beginning; and not Paul either, I think. I'm pretty certain this is the 'rude' version I remember, since that's what I remember him saying.
Anyway. One for the geeks.