A food critic was someone who criticized others' preparation of food.
Sometime prior to 2372, Quark served as a cook aboard a Ferengi freighter. He used to carry a disruptor pistol because, in his words, "every member of that crew thought he was a food critic." (DS9: "The Way of the Warrior")
In 2373, Michael Eddington recalled Benjamin Sisko's preparation of a Thanksgiving dinner for the senior staff happily, adding that Sisko had put too much tarragon in the stuffing. Sisko replied, "I wasn't aware that you were a food critic." Eddington explained that he hadn't been until he joined the Maquis and began eating "real food" (homegrown vs replicated). (DS9: "Blaze of Glory")