Seek Out the Ashtongue

Make sure you do this BEFORE fighting Akama's Shade.

We knew that defeating Akama's Shade made the Broken friendly, which we figured would then let us talk to the questgiver--but, unless you're required to come here twice just for that (which seems incredibly redundant), you have to talk to the Broken first.

We defeated the Shade only to get a quest telling us to defeat the Shade... fun times. Thanks, Blizzard.

You need to go see [npc=23158] ignore what quest tells you

This is a quest involved in the Black Temple Attunement Chain:

The Black Temple attunement starts at The Altar of the Sha'tar for Aldors, and the Sanctum of the Sun for Scryers. Both are in Shadowmoon Valley.

Aldors start attunement from Anchorite Ceyla (http://www.wowhead.com/?npc=21402) at the Altar of Sha'tar in Shadowmoon Valley:
1. [A] http://www.wowhead.com/?quest=10568 [70] Tablets of Baa'ri
2. [A] http://www.wowhead.com/?quest=10571 [70] Oronu the Elder
3. [A] http://www.wowhead.com/?quest=10574 [70] The Ashtongue Corruptors
4. [A] http://www.wowhead.com/?quest=10575 [70] The Warden's Cage

Scyers start attunement from Arcanist Thelis (http://www.wowhead.com/?npc=21955) at the Sanctum of Stars:
1. [Sc] http://www.wowhead.com/?quest=10683 [70] Tablets of Baa'ri
2. [Sc] http://www.wowhead.com/?quest=10684 [70] Oronu the Elder
3. [Sc] http://www.wowhead.com/?quest=10685 [70] The Ashtongue Corruptors
4. [Sc] http://www.wowhead.com/?quest=10686 [70] The Warden's Cage

After that, the chain comes together for Aldor and Scryer.

5. http://www.wowhead.com/?quest=10622 [70] Proof of Allegiance
6. http://www.wowhead.com/?quest=10628 [70] Akama
7. http://www.wowhead.com/?quest=10705 [70] Seer Udalo

Seer Udalo is found in the Arcatraz (http://www.wowhead.com/?zone=3846) just before the last boss.

8. http://www.wowhead.com/?quest=10706 [70] A Mysterious Portent
9. http://www.wowhead.com/?quest=10707 [70] The Ata'mal Terrace
10. http://www.wowhead.com/?quest=10708 [70] Akama's Promise

After you finish this chain, you get to pick from some rewards and the chain seems like it ends. It continues however, inside Serpentshrine Cavern (http://www.wowhead.com/?zone=3607) from an NPC called Seer Olum (http://www.wowhead.com/?npc=22820) who you can speak with after killing Fathom-Lord Karathress. He starts the next part of the Black Temple Chain by offering the quest:

1. http://www.wowhead.com/?quest=10944 [70] The Secret Compromised
For this quest you just return to Akama.
2. http://www.wowhead.com/?quest=10946 [70] Ruse of the Ashtongue
In this quest, you must use the costume Akama provides, and kill A'lar in Tempest Keep: The Eye while wearing the Ashtongue Cowl. Attunement for The Eye is a whole different chain.
3. http://www.wowhead.com/?quest=10947 [70] An Artifact From the Past
In this, you need to gain access to The Battle of Mount Hyjal in Caverns of Time, and slay the first boss, Rage Winterchill. Attunement for this involves killing Lady Vashj and Kael'Thas Sunstrider.
4. http://www.wowhead.com/?quest=10948 [70] The Hostage Soul
For this you must speak with A'dal in Shattrath city.
5. http://www.wowhead.com/?quest=10949 [70] Entry into the Black Temple
For this, just speak with the naaru Xi'ri in front of Black Temple.
6. http://www.wowhead.com/?quest=10985 [70] A Distraction for Akama
Unknown what this quest asks of you, most likely you need to defend Xi'ri and make your way into Black Temple. At the end, you become attuned to enter and are granted The Medallion of Karabor (http://www.wowhead.com/?item=32649)

At this point, you are attuned and can enter Black Temple, although the chain continues and you can soon upgrade your medallion. It continues with:

1. http://www.wowhead.com/?quest=10958 [70] Seek Out the Ashtongue
You just need to find Seer Kanai (http://www.wowhead.com/?npc=23158) inside Black Temple.
2. http://www.wowhead.com/?quest=10957 [70] Redemption of the Ashtongue
This involves entering Black Temple, and killing the boss the Shade of Akama (http://www.wowhead.com/?npc=22841).
3. http://www.wowhead.com/?quest=10959 [70] The Fall of the Betrayer
After killing the Shade of Akama and returning to Seer Kanai, he asks one last thing of you. Kill Illidan The Betrayer. After doing so, you are granted the Blessed Medallion of Karabor, an upgraded version of your original medallion, and allows teleportation to the Black Temple.