Making the Quesadillas:

1. Preheat the broiler. Place the chiles on a baking sheet and broil, turning as needed, until the skins blacken and blister. Do not over cook as they will fall apart. Remove from the broiler, drape loosely with aluminum foil, let cool, then peel away the skins. Cut the chiles in half lengthwise, remove and discard the seeds and stems and finely dice or cut into long, thin strips.

2. Place the flour tortillas in a single layer on a work surface. Scatter about 1/4 cup of the cheese over half of each tortilla. Top with the chiles and green onion, dividing them evenly. Sprinkle with salt and pepper. Carefully fold each tortilla in half. Do not press down on them or they may crack.

3. Heat a stove-top grill pan or a heavy frying pan over medium heat. Lightly oil the pan.

4. Place as many tortillas as will fit on the plan without crowding and weight them down with a pan lid or the bottom of another pan. Cook until golden brown on the first side, about 4 minutes. Carefully flip them over, use the lid again to weight them down and cook on the second side until golden and the cheese is melted, about 4 minutes longer. Remove from the griddle or pan and keep warm. Repeat with the remaining filled tortillas.

5. Cut each filled tortilla in half, sprinkle with the cilantro leaves and serve.