How can I edit the WooCommerce Mini DropDown Cart to read as follows

You can use the following function and filter hook

function filter_woo_cart_quantity($output, $cart_item, $cart_item_key){
        return '<span class="quantity">' . sprintf( '%s &times; Quote', $cart_item['quantity'] ) . '</span>';
    }
add_filter('woocommerce_widget_cart_item_quantity','filter_woo_cart_quantity',10, 3);