nodejs https.request -- how to send UTF-8 characters / set encoding?

Using nodejs https.request, we're making a POST request with contents request.write(JSON.stringify(data))

One of the characters in request body is '£'. When this is present, the server responds with unexpected token at '... ��...'

Adding utf-8 to content type doesn't make any difference: 'Content-Type': 'application/json; charset=utf-8',

How to fix this? Or, how can one set encoding for https.request content, if it's not already UTF-8?

Related question: Module request how to properly retrieve accented characters? � � �

Maybe this could work:

// Setup the request.  The options parameter is
// the object we defined above.
var req = http.request(options, function(res) {

  // Set the correct encoding of the data
  res.setEncoding('utf-8');

  var responseString = '';

  res.on('data', function(data) {
    responseString += data;
  });

  res.on('end', function() {
    var resultObject = JSON.parse(responseString);
  });
});

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