If using canned pineapple, drain the liquid and blot the ring with a paper towel to soak up excess moisture.
In a small bowl, combine the mustard and mayonnaise.
Slice the rolls in half, and spread the mixture over each half.
Cut the ham slices in half, then fold each half into quarters. Place a folded ham quarter over each roll half, top two of those with a pineapple ring and top with sliced cheese to close the rolls.
For a packed lunch:
Place the sliders into a lunch container, and add the veggies and dip to the empty compartments. Close the container and pack it into a lunch bag with an ice pack.