Coole Idee. Meine war genau anders herum.
(copy&paste von woanders, daher auf englisch:)
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Agarthi was once a powerful empire, its center located under the Gobi desert is. It was ruled by a race of snake people, but with a few humans in the "middle management", and lots and lots of human slaves. The reasons are unknown, but one day all the snake people retreated to the underground part of their kingdom and sealed all the entrances, leaving the humans stranded on the surface. Under pressure from surrounding human barbarians, the Agarthi retreated to their core land, mighty mountain fortresses in the Gobi desert, where they remain - mostly unknown - until today (today = 1245AD).
They trade with human settlements at the edge of the desert (gold and diamonds for food and slaves, mostly), and from time to time man one of their smaller fortresses there and use them as trade posts.
There is a centuries old struggle between the faction that wants to remain in the desert and await the return of their snake masters, and the faction that want to "abandon the old ways" and conquer a little bit of more hospitable land, with smaller factions siding with one or the other as they can gain politically from it. But the argument has become more heated, and a few "suspicious deaths" among powerful figureheads have happened.
All of this is unknown in Karakorum, there are only a few unreliable rumors of a mighty kingdom in the desert. But there isn't much else to do, so Töregene Kathun sends out a small diplomatic mission, to locate and find this kingdom, establish contact, and - depending on what they find - demand submission and tribute, raid, or spy the defenses for future campaigns.
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Also die SCs als Anführer dieser kleinen diplomatischen Mission (~paarhundert Reiter), die Kontakt mit Agarthi aufnehmen und sich schön in die Ränkespiele einmischen können.
Und so eine Agarthi-Festung sieht ungefähr so aus (den Schuttkegel am unteren Rand wegdenken):
