Smoked Chicken Quesadillas with Cilantro and Pepper Jack Cheese

Quesadillas are often described as Mexican grilled cheese sandwiches, but the truth is that most Mexicans cook quesadillas by deep-frying or pan-frying them. So leave the grilling to us. Like so much in our food culture, we Americans not only embrace the specialties of our neighbors and immigrants, we transform them and make them our own. These quesadillas explode with barbecue flavor—from the smoked chicken, from the pepper Jack cheese, and of course, from charring the quesadillas on the g