Put half the beans in a bowl and mash them roughly with a fork. Add the remaining beans, corn, pepper, green onions, cumin, paprika, salt and lime juice, and stir.
Lay the tortillas flat. Sprinkle a quarter of the cheese over one half of each, top with a quarter of the bean mixture, then fold the empty half over and press gently.
Heat a large skillet over medium heat and brush lightly with oil.
Cook 1 or 2 quesadillas at a time for 2–3 minutes per side, pressing with a spatula, until the tortillas are golden and the cheese has melted.
Let them rest for 1 minute, then cut into wedges and serve with salsa and avocado.