Make sure your cooked shredded chipotle chicken thighs are warm. If they're cold straight out of the fridge, heat them slightly in a pan or in the microwave.
Layer the quesadilla
Lay a flour tortilla flat on your workspace. Sprinkle a generous, even layer of grated cheese over exactly one half of the tortilla. Add an even layer of the warm, shredded chicken directly on top of the cheese. Add another layer of cheese over the chicken. Fold the empty half of the tortilla over to close it like a half-moon.
Toast
Melt 1/2 tablespoon of butter in a large skillet over medium-low heat. Once the butter is bubbling but not browned, carefully place the folded quesadilla into the pan.
Crisp and melt
Cook slowly for 3 to 4 minutes on the first side, until deep golden brown and crispy. Slide a large spatula under the quesadilla, holding the top edge closed with your other hand or tongs, and flip. Cook 2 to 3 minutes more, until the second side is golden and the cheese is visibly oozing from the edges.
Rest and serve.
Remove from the pan and place on a cutting board. Let rest for exactly 1 minute. Cut into wedges and serve immediately with pico de gallo and sour cream on the side.
Notes
Chicken cut: boneless, skinless chicken thighs only. The higher fat content keeps the meat juicy under the skillet's second round of heat; shredded breast dries out and turns powdery.
The "glue" method: cheese layered on both the top and bottom of the chicken is what holds the fold together through the flip.
Grate your own cheese. Bagged pre-shredded cheese is coated in cellulose, an anti-caking agent that keeps it from melting into a smooth layer.
Keep wet ingredients outside. Pico de gallo and sour cream go on the side, never inside the fold, or their moisture steams the tortilla soggy.
Storage: airtight container, refrigerated, up to 3 days.
Reheating: dry skillet over medium-low heat, 2 to 3 minutes per side, or air fryer at 350°F (175°C) for 3 to 4 minutes. Skip the microwave, it turns the tortilla tough and rubbery.