Way of the Wok

Cooking specializations can be learned starting at level 530 from Sungshin Ironpaw, in the Halfhill Market in the Valley of the Four Winds. What's not mentioned, is unlike alchemy, or the now defunct tailoring specializations, you can specialize in each form of cooking, and all at the same time. So, save up your raw materials while you're out leveling, because you can find a use for them in one of the specializations.

Each specialization increases one primary stat, except for the Way of the Brew, which provides mana replanishing drinks, and apparently headaches and grandeur. Each quest requires something specific to start; these items are returned to you at the end of the quest, and are needed for the first quest in each specialization to get an Ironpaw Token.

Way of the Wok: increases agility
Requires 5 juicycrunch carrots and is turned in to Anthea Ironpaw
Examples: Sauteed Carrots, Valley Stir Fry

Way of the Steamer: increases spirit
Requires 5 giant mantis shrimp and is turned in to Yan Ironpaw
Examples: Fire Spirit Salmon, Shrimp Dumplings

Way of the Pot: increases intellect
Requires 5 jade lungfish and is turned in to Mei Mei Ironpaw
Examples: Swirling Mist Soup, Braised Turtle

Way of the Oven: increases stamina
Requires 5 wildfowl breasts and is turned in to Jian Ironpaw
Examples: Chun Tian Spring Rolls, Twin Fish Platter

Way of the Gril: increases strength
Requires 5 raw tiger steaks and is turned in to Kol Ironpaw
Examples: Eternal Blossom Fish, Black Pepper Ribs and Shrimp

Way of the Brew: mana drinks, some also replenish health
Requires 1 ginseng and is turned in to Bobo Ironpaw
Examples: Mad Brewer's Breakfast, Ginseng Tea

Even though you get this quest in Valley of the four winds, I wouldn't suggest farming the Virmen in that zone. You're better off killing the trolls in Kun-lai summit. Don't bother farming mobs. I killed a bunch of zandalari and didn't get anything. Maybe my RNG is bad but this seems the least efficient way to get the carrots.

Conversely, you could also purchase a sack containing 25 of them from [npc=64395], located at Halfhill in Valley of the Four Winds. Only costs 1 token so to be perfectly honest I'm going with this option.. lol. (and also farming it by planting/harvesting) You can easily obtain tokens by farming meat, turning a stack of 20 into a bag of groceries and turning in that bag for 1 token... pretty quick this way if you just pick 1 type of meat to farm.

EDIT: I noticed people were upvoting this comment so I double-checked my information because there's a lot of confusion as to where the best place to get these darn carrots is.

As a quick note to those of you having trouble learning all of the cooking sub-proffessions (ie, way of the wok, way of the steamer, etc. etc.)

If you get 1 ironpaw token from finishing any of these quests, you can cash it in at the vendor ([npc=64395], located on the south side of the path in the center of halfhill, to the west of the in) for a sack of whichever good you need for the quest, and then the quest gives you an ironpaw token, leaving you right where you started before you completed the quest. Essentially, if you get one done you can finish them all with a single ironpaw token:

As an example, 1 ironpaw token buys you Juicycrunch Carrotx25 (contained within [item=87707] from [npc=64395]), which you can trade in 5 of to finish this quest, getting you back your token + 15 carrots, and you have the quest done. Then you use the ironpaw token to buy the sack for the next quest, and so on and so forth. The only issue is you still have to get one of the sets of goods. I find the easiest to get to be the Wildfowl Breastx5 which you can get from the [npc=59641] that fly directly over halfhill. These can be turned in right in halfhill to [npc=58716]