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 on top, followed by the marinara, mozzarella, and basil. Top with the remaining rolls.
Mix the melted butter in a small bowl with the garlic, parsley, and Parmesan. Brush the tops of the rolls with the butter mixture. Bake for 20 minutes, or until the bread is golden brown. Slice into individual sliders, then serve.