In the internally famous Google video, Broccoli Man was the jaded production-savvy SWE/SRE who told the earnest SWE (Panda Woman, I think?) what hoops she needs to jump through to launch her service. Among the most famous lines: her "I just want to serve 5TB of data" to his "I forgot how to count that low".
The video had a huge impact because it was funny and had more than a little bit of truth to it. Lots of Google infrastructure was oriented toward huge problems and required the same heavyweight processes for things that aren't so huge. It inspired a bunch of changes to simplify deploying small (by Google standards) services. Many small things are still difficult at Google, but a bit less so now.
I've only said and heard "I forgot how to count that low" as a reference to this video, making fun of the unexpected difficulty of doing something small rather than actually making fun of someone for wanting to do something small.
The video was also described briefly here: https://rachelbythebay.com/w/2012/04/06/5tb/
But yeah, that video was epic, and it was spot-on, too. A company that has no idea how to deal with people is going to suck at making tools _for_ people.
So maybe 'broccoli' is their way of saying craziness? Like being on Google drugs. But obviously that's not a perfect fit. Maybe its a misspelling of something else?