Ok, here's the breakdown:
There are 4 tiers of crafting skills:
1-20 is Apprentice
21-40 is Journeyman
41-60 is (Expert I think)
61-80 is (Master i think)
Currently, master isn't available yet (no 61-80 recipes yet). When you max a skill in its tier, you have to complete a quest to advance that craft to the next tier before you can level it further. Only 6 crafts can be raised to Journeyman and only 3 of those can be raised to Expert (and 1 of those can be raised to Master when it is released). So you have to raise cooking to Journeyman rank before you'll gain more exp in it.
Also, keep in mind that the limits for each tier also apply to the 3 gathering skills and planting. In other words, you have 10 crafting skills all together: Planting, Herbalism, Woodcraft, Mining, Alchemy, Cooking, Armorcraft, Blacksmithing, Carpentry, Tailoring. Only 6 of those can go past lvl 20 (pending completion of relevant quest) and only 3 can go past 40 (also pending quest).
So to advance Cooking to the next tier, go to Varnas or Obsidian and speak to the cooking trainer.