MMOMinion

I took this from here http://www.ffxivguild.com/ffxiv-end-game...ster-star/, and made a quick profile from it. It's not 100% HQ, from my guessing it's like 50-60%, but at least it's afk'able for food. Using HQ mats helps obviously. Check your cross skills before using. I use this with fully melded gear and lvl70 head and tool.
Probably usable for other classes too...
Use Boullabaise HQ.

Statistics: 76HQ 16NQ of Popoto Pancakes. A bit more than my estimated 50-60% ;)