Installation on Linux is trivial, just download docfx.zip, unzip wherever you want (I used ~/docfx/) and add this little script (call it docfx and give it execution permission) somewhere in your path:

#!/bin/bash
mono ~/docfx/docfx.exe $@

Then, in your EFL checkout:

docfx init

Answer all questions (I used the default folder docfx_project, set the source directory to ../src and the files Glob pattern to lib/efl_mono/libefl_mono.dll).
To be sure, after running docfx init, the top of your docfx_project/docfx.json file should be similar to this:

{
  "metadata": [
    {
      "src": [
        {
          "src": "../src",
          "files": [
            "lib/efl_mono/libefl_mono.dll"
          ]
        }
      ],

Then you run:

docfx docfx_project/docfx.json

And, after 20 minutes of process and consuming about 2GB of RAM, it uses up 600MB of hard drive. Most of this disk space is used for caches, the actual HTML folder (_site by default) is about 90MB. A second run after modifying a single cs file took "only" 5 minutes.
If you then open _site/api/index.html with a browser, you can see our classes in all their glory. It's got the usual Collapsible Site Navigation left side bar (including a search box), the page TOC right side bar (with auto-highlight as you scroll), inheritance graphs, internal links, etc.

Screenshot attached for your convenience.

Next step is to start customizing it to see if it fits all our needs.

A branch has been created with the tests: devs/xartigas/docfx-support
Some notes about the tasks:

• Filter out unwanted API (legacy, ...)
  • Easy enough using the filter keyword as shown in the testing branch.
• Check that cross referencing works (links to other APIs, methods, ...)
  • Automatic method linking is pending on T7453
• Add tutorials and programming guides
  • Section headers in DokuWiki create anchors named #The_Space_Box whereas in DocFx they are named #the-spacer-box. All section links in md files will need to be changed.
  • Links to other documents do not need to change much if we use the same folder structure.
  • DokuWiki headers need to be removed from every md file.