Preheat the oven to 425°F (220°C) and lightly brush a baking sheet with olive oil.
In a mixing bowl, combine the shredded chicken with dried basil, dried oregano, and garlic powder; toss until evenly coated.
Place two tortillas on the prepared baking sheet. Spread a few tablespoons of marinara sauce evenly on each tortilla, then sprinkle with a little of the shredded cheese.
Divide the seasoned chicken between the two tortillas, spreading it over the cheese, then add another light sprinkle of cheese on top of the chicken.
Top each with a second tortilla to make quesadillas and bake for 6 to 8 minutes, until the bottoms are just golden.
Carefully flip each quesadilla, then spread more marinara on the top of each and sprinkle with more shredded cheese; add pepperoni slices as desired.
Return to the oven and bake another 6 to 8 minutes, until cheese is melted and edges are golden and crisp.
Remove from the oven, sprinkle with grated Parmesan and torn fresh basil, slice into wedges, and serve.