Slice the rolls in half lengthwise. Place the bottom half in a 9 x 13-inch (23 x 33 cm) rimmed baking dish. Spread the chicken evenly over the rolls, followed by the barbecue sauce, red onion, Pepper Jack cheese, and parsley. Top with the remaining rolls.
Brush the tops of the rolls with melted butter. Bake for 20 minutes, until the bread is golden brown. Slice into individual sliders, then serve.