How do I make a RESTful call in Unity with WWW?

Question

I've got a Unity game that I'm working on which needs to make calls to a RESTful API (meaning that I need to make GET, POST, PUT, and DELETE calls). I'm trying to use the WWW class to make these calls as shown below, but it's not working:

public class GameRegistry : MonoBehaviour {
    public string SERVER = "my.ip.address.here/connections";

    private static string METHOD_HEADER = "X-HTTP-Method-Override";
    private static string CONTENT_HEADER = "content-type";
    private static string CONTENT_TYPE = "application/json";

    public void Start()
    {
        Debug.Log("Starting...");
        RESTHelper(SERVER, "", "DELETE");
        Debug.Log("...Finishing.");
    }

    private IEnumerator<WWW> RESTHelper(string url, string payload, string method)
    {
        Dictionary<string, string> headers = new Dictionary<string, string>();
        headers.Add(METHOD_HEADER, method);
        headers.Add(CONTENT_HEADER, CONTENT_TYPE);

        Debug.Log("Request sent...");
        WWW request = new WWW(url, Encoding.UTF8.GetBytes(payload), headers);
        yield return request;
        Debug.Log("...reponse received.");
        Debug.Log(request.text);
    }

When I attach this to a GameObject and run it in my game, I get the following output:

Starting...
...Finishing.

Nothing appears to be executed in the helper method. What am I doing wrong?

FWIW, I have tested the API with ARC and it works perfectly.