Preheat oven to 375°F and lightly grease a 9×13" baking pan. Set aside.
Add unwrapped package of rolls to your cutting board and using a serrated knife (like a bread knife), carefully slice across the rolls, horizontally, keeping one hand on top of the rolls to steady them.
Once sliced, keep the rolls connected to each other and lift the entire top section off of the bottom section. Add the bottom section of the rolls to the prepared baking pan.
In a small mixing bowl, combine melted butter, minced garlic, and parsley. Set aside.
Spread half of the pesto over the bottom half of the rolls in the baking pan.
Add shredded chicken on top of the pesto, then top that with the shredded cheese.
Spread remaining pesto over the cut side of the top half of the rolls, then add top half of rolls, cut side down, on top of the cheese.
Brush garlic butter mixture over the top of the rolls, then sprinkle with salt and pepper if desired.
Cover loosely with foil and bake in preheated oven for 10 minutes. Uncover and bake another 5-10 minutes, or until hot and cheese is fully melted.