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Yes at skill of 225 (level does not matter), you get this quest:
Correction: Your character level DOES mater. The quest used to require your character to be level 40, but recently Blizzard changed this level requirement, along with fishing and first aid, to be level 35.
So, if you have 225 cooking and your character is level 35 or higher you should be able to pick up this quest from the goblin in Gadgetzan.
Just a small suggestion:
While the rocs in that zone drop the giant eggs you need for that quest, I always find it easier and faster to get the eggs from owlbeasts in the Hinterlands. There tend to be less adds there and the owlbeasts seem to drop the eggs more frequently.