Preheat the air fryer to 180°C. In a large mixing bowl, combine the grated cheddar, chopped chorizo, diced tomatoes, sliced spring onions, red chili, and parsley. Drizzle with lime juice and mix until evenly incorporated.
Lay out the flour tortillas and distribute the filling evenly over one side of each. Fold the tortillas in half, pressing gently to secure the filling, ensuring it reaches close to the edges without spilling out.
Arrange the quesadillas in a single layer inside the air fryer basket, allowing slight overlap if necessary. Place a heatproof utensil on top to prevent them from opening during cooking. Air fry for approximately 10 minutes, flipping halfway through, until golden brown and crisp.
Remove from the air fryer and serve immediately with fresh lime wedges on the side. Enjoy warm for the best texture and flavor.