Preheat oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.
Slice the entire slab of rolls in half horizontally to create a top and bottom section.
Place the bottom half of the rolls into the prepared baking dish.
In a medium bowl, combine shredded chicken and basil pesto until the chicken is thoroughly coated.
Distribute the pesto chicken evenly over the bottom layer of rolls.
Place mozzarella cheese slices over the chicken to cover the entire surface.
Place the top half of the rolls back onto the cheese layer.
In a small bowl, whisk together melted butter, minced garlic, Parmesan cheese, and dried oregano.
Brush the garlic butter mixture generously over the tops of the rolls.
Cover the dish with aluminum foil and bake for 10 minutes.
Remove the foil and bake for an additional 10 minutes, or until the cheese is melted and the tops are golden brown.
Let rest for 5 minutes before slicing into individual sliders and serving.