This won't be too helpful as it's been a few years since we used the
DDP, but Min & Bill's is one of our favorites!!
I remember getting the Italian sand, chips, and a chocolate shake (more like a Wendy's Frostie than a shake). So somewhere in that mix, there had to be either a dessert or a drink. I'm thinking I got a bottled water and the shake was my dessert, but I'm not even 90% sure on that one.
If you decide to go there, I would just ask if you can have the shake as your dessert and get another drink instead of the cookie.