Hi onion, I would agree with Ophelia, I used CC with both my DC and both times it worked very quickly, BUT I at no stage left them to cry for 15 mins at a time, which sounds like pure torture for both you and her.
I can't remember if the method I used had a different name perhaps, but this is what we did:
Quite strict bedtime routine with bath, bottle, story, kiss and cuddle then lights out and 'goodnight DC' and leave the room
after 2 mins, lights off still, pick up, kiss and cuddle, then 'goodnight' and go outside
After another 2 mins, lay DC back down if needed, shhhhh, pat on the back 'goodnight' and outside again
After another 2 mins, return to lying down and pat but no verbal cues at all and no eye contact
After another 2 mins simply return gently to lying down and leave the room
Repeat final stage until successful. 
I found that both DC slept better within about a week. They also worked out pretty quickly that a) I was outside the door and would come back if they really needed me and wasn't going to ignore them but also b) that I wasn't going to cuddle them to sleep
It really did work for us and felt like the kindest thing for everyone. I was not coping AT ALL with sleep deprivation and they were knackered too and needed to learn how to self-settle. I know CC gets a bashing on mn sometimes, but IME it's not cruel or damaging, and can be a quick and easy way of getting to a contented self-settling child. Both my DC now sleep 12 hours straight and go straight to sleep at bedtime which I have to say is one of the main reasons DH and I are still (reasonably) sane 
Good luck!