Heat the large non‑stick skillet over medium‑high. While that’s coming up to temp, lightly butter one side of each tortilla.
Place one tortilla butter‑side down in the hot skillet. Add ⅓ cup shredded mozzarella, then 2 tablespoons pizza sauce, then the halved pepperoni (and basil if using). Sprinkle the remaining cheese, then top with the second tortilla, butter side up.
Let it cook 2‑3 minutes until the bottom tortilla is browning and the cheese is starting to melt. Carefully flip the entire quesadilla and cook until the second side crisps and the cheese is fully melted. Slide it onto a cutting board and cut into wedges while it’s still hot.