Preheat oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish or line it with parchment paper.

Without separating the rolls, use a serrated knife to slice the entire slab horizontally. Place the bottom half in the prepared baking dish.

In a mixing bowl, combine the cooked chicken, Alfredo sauce, Italian seasoning, and black pepper until the chicken is evenly coated.

Sprinkle half of the mozzarella over the bottom rolls. Spread the chicken Alfredo mixture evenly over the cheese, then top with the remaining mozzarella and 1/2 cup Parmesan.

Place the top half of the rolls over the filling and gently press into place.

Combine melted butter, garlic, Italian seasoning, and 1 tablespoon Parmesan. Brush evenly over the tops of the rolls.

Cover loosely with foil and bake for 15 minutes. Remove the foil and bake for another 8–10 minutes, until the cheese is melted and the tops are golden.

Rest for 5 minutes, sprinkle with parsley if desired, then cut along the roll seams and serve warm.