This sounds like a distorted memory of “Cowabunga,” a catchphrase associated with Cookie Monster on Sesame Street starting in the 1970s. The closest documented source I found says Cookie Monster used “cowabunga” enthusiastically, not “boonga boonga battery faaaaaaaaaaaace.”

Likely origin

  • “Cowabunga” originated earlier in children’s TV and later became a surfing/excitement exclamation.
  • Cookie Monster began using it on Sesame Street in the 1970s.
  • The phrase you heard is probably a misremembered or meme-ified version of that catchphrase.

What I could confirm

  • I found a Sesame Street video about Cookie Monster losing a cookie, but nothing matching the exact quote you typed.
  • The search result that best matches the “Cookie Monster catchphrase” angle points to “cowabunga,” not the battery/face line.

Source shape

Claim| Evidence
---|---
Cookie Monster used “cowabunga”| Documented in the Muppet wiki source 1
The phrase likely isn’t an official quote| No matching official source found; closest match is “cowabunga” 19

TL;DR: it’s most likely from Cookie Monster’s “cowabunga” catchphrase on Sesame Street , not a real line about “boonga boonga battery faaaaaaaaaaaace.”