The above solution is good if you need it as a temporary solution…
For a long term, change your user settings in:

File -> Preferences -> Settings

Scrool Down until you will see:

Files(14) - number might be different

There you would see text like:

// Configure file associations to languages (e.g. “*.extension”: “html”).
These have precedence over the default associations of the languages installed.
“files.associations”: {},

Press edit → it should copy settings automatically to the right screen where you have USER settings.
Change to:

“files.associations”: {“*.html.eex”: “html”}

Save and Close File with settings

Test that it works

If you use the vscode-elixir-ls extension, note that EEx-related settings may need to change due to recent updates. With the latest version of that package, capitalize the second E:

"emmet.includeLanguages": {
  "HTML (EEx)": "html"
}

I was able to get emmet working in VSCode with the following setting:

"emmet.includeLanguages": {
    "HTML (Eex)": "html"
}