Smoke the chicken thighs at 250°F (120°C) for 2-3 hours, or until internal temperature reaches 165°F (74°C). Let cool and shred.
Season the shredded chicken with smoked paprika, brown sugar, chili powder, cumin, cayenne pepper, garlic powder, onion powder, salt, and pepper.
Roast the poblano peppers over an open flame until blackened on all sides. Place in a bowl, cover with plastic wrap, and let steam for 10 minutes. Peel, seed, and dice.
Prepare the Poblano-Corn Relish: Combine diced poblano peppers, corn kernels, red onion, cilantro, and lime juice in a bowl. Mix well.
Combine all Sauce ingredients in a bowl and mix well.
In a separate bowl, combine the shredded chicken and Sauce. Mix until well coated.
Lay out a tortilla and sprinkle half of it with the Oaxaca cheese. Top with a portion of the smoked chicken mixture and the Poblano-Corn Relish. Sprinkle with Queso Fresco.
Fold the tortilla in half.
Heat clarified butter in a large skillet over medium heat. Cook the quesadilla for 3-4 minutes per side, or until golden brown and the cheese is melted.
Repeat with remaining tortillas and filling. Serve immediately.
