Demo: https://anchor.host/2016/03/07/hacking-wp-engines-web-based-wp-cli/

wp_engine_cli.php

<?php

###  PHP command line wrapper for WP Engine's web based WP-CLI
###  Example command line: php wp_engine_cli.php -i wp_install_name -c "cli info"

# Grab options from command line
$options = getopt("i:c:");

# Break out into variables
$install = $options["i"];
$command = $options["c"];

# Replay token and cookie from valid WP Engine web request
$token = "######";
$cookie = "######";

$curl_url = "https://my.wpengine.com/installs/$install/wp_cli?command=" .urlencode($command);

$curl = curl_init();

curl_setopt_array($curl, array(
  CURLOPT_URL => $curl_url,
  CURLOPT_RETURNTRANSFER => true,
  CURLOPT_ENCODING => "",
  CURLOPT_MAXREDIRS => 10,
  CURLOPT_TIMEOUT => 30,
  CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
  CURLOPT_CUSTOMREQUEST => "POST",
  CURLOPT_HTTPHEADER => array(
    "cache-control: no-cache",
    "cookie: $cookie",
    "x-csrf-token: $token"
  ),
));

$response = curl_exec($curl);
$err = curl_error($curl);

curl_close($curl);

if ($err) {
  echo "cURL Error #:" . $err;
} else {

  # convert json output to PHP array
  $array = json_decode($response, true);

  # output reponse from array back to command line
  echo $array["response"];
}