The most recent of lectures about GR as a QFT are those of the TRISEP school hosted at the Perimeter Institute in July 2018. I am giving 4.5 hours of lectures here to students who span the experimental and theoretical aspects of fundamental physics.
I am using this page to give the lecture notes and related materials for this course. Folks interested in more detail can access my EPFL lectures ( covering 14 hours total) from 2016. These have been written up and posted on the arXiv with the help of Mikhail Ivanov and Andrei Shkerin. Finally I gave a semester-ong course on this topic in 2015, and the notes are available here. ( Note that UMass has changed their cloud storage procedure, so that the video links do not presently work. I have the files saved and hope to re-post them using a different storage system.)
Lecture 1 Effective Field Theory