add_filter('woocommerce_add_to_cart_fragments', 'custom_cart_fragment');
function custom_cart_fragment($fragments) {
    ob_start();
    ?>
    <span class="custom-cart-item-count"><?php echo WC()->cart->get_cart_contents_count(); ?></span>
    <?php
    $fragments['span.custom-cart-item-count'] = ob_get_clean();
    return $fragments;
}