In a medium bowl, whisk together the mayo, jalapeño juice, minced jalapeños, garlic powder, cumin, paprika, and cayenne. Season with kosher salt, and place in the fridge until you're ready to use it.
For the Quesadillas
In another medium bowl, add the cooked, shredded chicken. Toss the chicken with half of the quesadilla sauce. Set the rest aside for dipping. (Omit this step if someone has a sensitivity to spicy foods.)
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 the 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 this process with the remaining ingredients to make 3 more quesadillas. Slice into wedges and serve warm with remaining sauce for dipping.
If you don't have pre-cooked chicken, simply boil boneless skinless chicken breasts for about 20 minutes, and shred with two forks. I like to use the pre-cooked rotisserie chicken from my local supermarket to save time.
This can be a vegetarian meal by omitting the chicken altogether.