Stir the carrot puree into the pizza sauce until fully blended.
Lay out four tortillas on a clean surface and spread the sauce mixture evenly over each one.
Sprinkle the mozzarella cheese and chopped pepperoni over the sauce, then add a light dusting of Italian seasoning.
Top each with a second tortilla and press down gently so the fillings stay in place.
Heat 1 tablespoon of olive oil in a large skillet over medium heat.
Cook one quesadilla at a time for 2 to 3 minutes per side until the tortillas turn golden and the cheese melts.
Repeat with the remaining quesadillas, adding the second tablespoon of oil as needed.
Slice each quesadilla into wedges before serving.