FOR THE SAUCE
1 c. mayonnaise
3 tbsp. juice from jar of pickled jalapeños
3 tbsp. minced pickled jalapeños
2 tsp. garlic powder
2 tsp. cumin
2 tsp. paprika
1/2 tsp. cayenne
FOR THE ASSEMBLY
8 medium flour tortillas
4 c. shredded chicken
2 c. shredded Monterey Jack
12 slices American (or cheddar) cheese
Make sauce: in a medium bowl, whisk together mayo, jalapeño juice, minced jalapeños, garlic powder, cumin, paprika, and cayenne. Season with kosher salt.
To another medium bowl, add chicken. Toss chicken with half of the quesadilla sauce. Set the rest aside for dipping.
In a large skillet over medium-high heat, add a flour tortilla. Top with 2 slices of American cheese and ½ cup chicken, then sprinkle with ½ cup Monterey Jack. Place second tortilla on top. Cook until the bottom tortilla is golden, about 2 minutes, then flip and cook until the second tortilla is golden and the cheese has melted, about 2 more minutes.
Repeat process with remaining ingredients to make 3 more quesadillas. Slice into wedges and serve warm with remaining sauce for dipping.