Setting processData to false in jQuery breaks my AJAX request

You want to pass the data as JSON. You are passing a Javascript object. JSON is a way of serializing Javascript objects to strings so that they can be passed around without compatibility issues.

You actually want to pass the JSON in a string:

$.ajax({
    url: myUrl,
    type: "POST",
    data: '{"foo": "bar"}',
    processData: false,
    contentType: 'application/json'
});