Slice the Hawaiian rolls in half horizontally to separate the tops from the bottoms. Place the bottom halves in a baking dish and keep the tops aside.
Preheat your oven to 350°F. In a small bowl, mix the Dijon mustard, mayonnaise, cayenne, and salt. Spread this mixture evenly over the bottom halves of the rolls.
Fold each slice of ham in half. Place two folded slices next to each other across the buns until they are fully covered.
Add a layer of shredded chicken on top.
Place the Swiss cheese slices over the chicken. Put the top halves of the rolls back on.
In another small bowl, combine the melted butter, minced garlic, salt, and parsley. Microwave the mixture for about 30 seconds or until the butter is melted.
Stir it well and brush it over the tops of the rolls.
Cover the baking dish with foil and bake for 30 minutes. Take off the foil and bake for another 5 minutes so the tops turn golden brown. Slice into individual sliders and serve warm.