Both Factions: Cooking Artisan Trainer

Go to Zamja in Ogrimmar (Horde), or Daryl Riknussun in Ironforge (Alliance) first, and accept the quest that sends you to:

The goblin in the inn, Dirge Quikcleave in Gadgetzan, Tanaris. He gives you a quest to complete to be able to up past 225 on your Cooking Skill.

Save yourself some effort and make sure you have 20 Alterac Swiss on you, you can't find them in Gadgetzan or anywhere near. You can find them from the cheese vendor in SW, or Innkeepers, Cooking Suppliers, Bartenders.

You will need 12 giant eggs, 20, Alterac Swiss, and 10 Zesty Clam Meat to complete the quest.