Retrieve Qilue's Brain - Baldur's Gate 2 Side Quest
The Retrieve Qilue's Brain side quest starts during and takes place in the middle of the Inside The Drow City side quest. After defeating the Beholder during the Inside The Drow City quest your next time visiting the entrance of Ust Natha you'll be approached by a Duergar who asks you to speak to his "master" in the nearby tank.
You technically have 2 options for this quest despite it seeming like you have no choices. The creature inside of the tank will threaten to blow your cover if you don't help it out but you're able to flip the tables on it and threaten to blow its cover which will resolve the quest on the spot for 12k EXP. I'd recommend against this route as you'll lose out on some items and EXP since you won't be able to enter Qilue's House without this quest.
If you choose to accept this task from the creature in the tank you'll need to visit Qilue's Home which is right above the Female Fighter's Society in the central portion of Ust Natha. Qilue's Home is marked on the map so you should have no issue at all locating it. Upon entering you'll immediately be attacked by any and all Drow inside of her home, for this reason I would recommend buffing up before heading inside.
Once inside you'll quickly learn that Qilue is not alone. There are about a half dozen Drow enemies in here with her and most of them are mages so be prepared for a tough fight on harder difficulties. When you defeat Qilue she'll drop a Boneblade +4 which is a magical dagger along with her brain which we need for this quest.
Returning Qilue's brain to the tank will net you 10,000 EXP in total which is less EXP than we got for clearing out Qilue's home. Oh well.