The cotton batting that I had bought was way too thick for the project, but also quite easy to take apart into layers.
First I cut the batting after the shape of the linen pieces, and then I pulled the layers apart.
I then pinned the second layer of linen on top of the batting. To secure it further I basted around all the edges, along the seams where the side gores are attached and from neck to hem in the middle. Helped by my trusted assistant Miss Esau (she's named after a cat in a Swedish comedy sketch, and we thought that we were going to have a boy cat again, but it works well for her too).
Then I removed to my couch and started quilting in front of the telly.
Apparently it is very tiring to help out.