I am a level 60 fire mage that just arrived in Outland and saw the cooking trainer. Question is where does one get the ingredients to do cooking in Outland to level up their cooking experience to get the first recipe which is level 20?
Outland profs in general went with a less trainer-based recipe system and more “find it out in the world” system.
You can buy the recipe for Ravager Dogs in your faction’s Hellfire town - look for Cookie One Eye (Horde) or Sid Lombardi for the Alliance. That can be learnt at Outland skill 1 and uses meat found in HFP.
You can also earn the recipe for Buzzard Bites from a short but tedious quest chain given by the goblins that crashed south of the Alliance town. In the course of earning the recipe you will also likely gather quite a bit of Buzzard meat to cook with it.
Outland recipes are all over the place.
https://www.wow-professions.com/guides/outland-cooking-leveling is a guide for leveling Outland cooking wowhead links to the recipes you will need. Wowhead will tell you who sells them.