Where did the phrase You "have a really punchable face" originate?

N.B. I'm just handling "punchable face" and taking the rest as decorative.

Based on transcript research (Google site:avatar.wikia.com/wiki/Transcript punchable - proper link to google site search omitted due to lack of rep), your memory regarding tLA may be faulty (or the transcripts are). In any case, a check on mspaintadventures tells us that page was first published on July 2, 2009, and all the tLA episodes came out in 2008 or earlier, so if tLA did use it, you're correct that it didn't come from MPA.

That's all moot, however, since the first (indexed) reference I could locate to the phrase itself being published is well before either, in a July 29, 2002 Guardian article by Alexis Petridis: "Ben Elton's punchable face singing along to All You Need is Love", and FumbleFingers found one even earlier (in the comments), in a 1995 book, Edsel: a Novel of Detroit.

Given the Guardian article was a music review, it seemed plausible the phrase is a corruption of "sockable face", in the song "Sockable Face Club", from the album Rapid City Muscle Car released by the Cherry Poppin' Daddies in 1994, but that's speculative, and the novel reference makes it seem slightly less likely.