Look deeper into the plugin documentations. No need for groovy here.
Just make sure Content Type is set to HTML and add the following to the body:
${FILE,path="my.html"}
This will place the my.html
content in your email body (location of file is relative to job’s workspace. I use it and it works well.
I hope this helps.
EDIT: Note that you must have the Jenkins version 1.532.1 (or higher) to support this feature with the email-ext plugin.