The code is in the live_reloader, as said by @dom, in the private functions…

At the very end, we can find

  defp before_send_inject_reloader(conn, endpoint) do
    register_before_send(conn, fn conn ->
      if conn.resp_body != nil && html?(conn) do
        resp_body = IO.iodata_to_binary(conn.resp_body)
        if has_body?(resp_body) and :code.is_loaded(endpoint) do
          [page | rest] = String.split(resp_body, "</body>")
          body = page <> reload_assets_tag(conn) <> Enum.join(["</body>" | rest], "")
          put_in conn.resp_body, body
        else
          conn
        end
      else
        conn
      end
    end)
  end

  defp reload_assets_tag(conn) do
    path = conn.private.phoenix_endpoint.path("/phoenix/live_reload/frame")
    """
    <iframe src="#{path}" style="display: none;"></iframe>
    """
  end

The solution is dead simple (once You get how it works), Not even the need to parse the static file, just render with.

  def index(conn, _params) do
    file = "priv/static/index.html"
    {:ok, binary} = File.read(file)
    html(conn, binary)
  end

The html helper will take care of this. Sorry for the question…

Now I have a slim api, with live reload enable on the static file.