You can use this small library: https://github.com/ledfusion/php-rest-curl

Making a call is as simple as:

// GET
$result = RestCurl::get($URL, array('id' => 12345678));

// POST
$result = RestCurl::post($URL, array('name' => 'John'));

// PUT
$result = RestCurl::put($URL, array('$set' => array('lastName' => "Smith")));

// DELETE
$result = RestCurl::delete($URL); 

And for the $result variable:

• $result['status'] is the HTTP response code

• $result['data'] an array with the JSON response parsed

• $result['header'] a string with the response headers

Hope it helps

For myself, I just encode it in the url and use $_GET on the destination page. Here's a line as an example.

$ch = curl_init();
$this->json->p->method = "whatever";
curl_setopt($ch, CURLOPT_URL, "http://" . $_SERVER['SERVER_NAME'] . $this->json->path . '?json=' . urlencode(json_encode($this->json->p)));
curl_setopt($ch, CURLOPT_HEADER, 0);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$output = curl_exec($ch);
curl_close($ch);

EDIT: Adding the destination snippet... (EDIT 2 added more above at OPs request)

<?php
if(!isset($_GET['json']))
    die("FAILURE");
$json = json_decode($_GET['json']);
$method = $json->method;
...
?>

I was Working with Elastic SQL plugin. Query is done with GET method using cURL as below:

curl -XGET http://localhost:9200/_sql/_explain -H 'Content-Type: application/json' \
-d 'SELECT city.keyword as city FROM routes group by city.keyword order by city'

I exposed a custom port at public server, doing a reverse proxy with Basic Auth set.

This code, works fine plus Basic Auth Header:

$host = 'http://myhost.com:9200';
$uri = "/_sql/_explain";
$auth = "john:doe";
$data = "SELECT city.keyword as city FROM routes group by city.keyword order by city";

function restCurl($host, $uri, $data = null, $auth = null, $method = 'DELETE'){
    $ch = curl_init();

    curl_setopt($ch, CURLOPT_URL, $host.$uri);
    curl_setopt($ch, CURLOPT_CUSTOMREQUEST, $method);
    curl_setopt($ch, CURLOPT_HTTPHEADER, array('Content-Type: application/json'));
    curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);

    if ($method == 'POST')
        curl_setopt($ch, CURLOPT_POST, 1);
    if ($auth)
        curl_setopt($ch, CURLOPT_USERPWD, $auth);
    if (strlen($data) > 0)
        curl_setopt($ch, CURLOPT_POSTFIELDS,$data);

    $resp  = curl_exec($ch);
    if(!$resp){
        $resp = (json_encode(array(array("error" => curl_error($ch), "code" => curl_errno($ch)))));
    }   
    curl_close($ch);
    return $resp;
}

$resp = restCurl($host, $uri); //DELETE
$resp = restCurl($host, $uri, $data, $auth, 'GET'); //GET
$resp = restCurl($host, $uri, $data, $auth, 'POST'); //POST
$resp = restCurl($host, $uri, $data, $auth, 'PUT'); //PUT