In order to become an Artisan cook, you'll need to complete a quest. Reach level 225 cooking and head to Gadgetzan.

1. Locate Dirge Quikcleave, he can be found in Gadgetzan. Pick up the quest Clamlette Surprise.
2. Alterac Swiss can be purchased in the Caverns of Time, southeast of Gadgetzan. Locate Galgrom , he's an orc and buy 20.
3. Head over to the Hinterlands and kill Owlbeasts to obtain 12 Giant Eggs. Owls in Felwood as well as Owlbeasts in Winterspring drop Giant Eggs also. Or, alternatively you can purchase them from an AH.
4. Zesty Clam Meat drops off various mobs in Azeroth, but for convenience the best place to pick them up is Tanaris. The coast near Steamwheedle Port has plenty of Steeljaw Snappers, these will drop your 10 clam meats.