I visited Jack and June recently on a Friday noon when there was no major arena event. I ordered the only sandwich choice, the Veggie Sammy which is marked vegan. It has avocado hummus, mushrooms, zucchini, squash, and red peppers served on ciabbata. I could taste that the sammy had been sauteed in butter. The manager offered to replace it and was apologetic that it had happened. It was good and would order again but be sure to mention not to use butter. I chose the side salad and hand-cut French Fries as sides. They were also good. Kudos for identifying the vegan and vegetarian options.
Cons: not many vegan choices, not vegan savvy