SE's own official database says otherwise :) http://na.finalfantasyxiv.com/...
I datamined the information for this (and thousands of other items) out of the game's files myself.
It's level 39. There is no level 36 Primary Culinarian tool. The closest is the 'white skillet' at level 34.
Do you have a screenshot showing that this, or some other item you're confusing it with, is level 36?