Example of how to override a JS method added by espresso_core.

tw_ee_my_events_cancel_link.php

<?php //Please do not include the opening PHP tag if you already have one

function tw_ee_override_espresso_core(){
    wp_add_inline_script( 
        'espresso_core',
        "jQuery(document).ready(function($){
            $.fn.extend({
                eeAddOverlay : function( opacity ) {
                    console.log('Testing');
                    opacity = typeof opacity === 'undefined' || opacity > 1 ? 0.5 : opacity;
                    var overlay = '<div id=\"ee-overlay\"></div>';
                    $(overlay).appendTo('body').css({
                        'position' : 'fixed',
                        'top' : 0,
                        'left' : 0,
                        'width' : '100%',
                        'height' : '100%',
                        'background' : '#000',
                        'opacity' : opacity,
                        'filter' : 'alpha(opacity=' + ( opacity * 100 ) + ')',
                        'z-index' : 10000
                    });
                    return this;
                }
            });
        });"
    );
}
add_action( 'wp_print_footer_scripts', 'tw_ee_override_espresso_core', 10 );