In a medium bowl, combine all Chicken ingredients and mix well to coat.
Heat 1 tablespoon of Olive oil in a large skillet over medium-high heat. Add the seasoned chicken and cook until cooked through, about 6-8 minutes. Shred the chicken with two forks.
In a separate bowl, combine the Monterey Jack cheese, pepper jack cheese, black beans, corn, and diced red onion.
In a small bowl, combine all Sauce ingredients and mix well.
Lay out a tortilla and sprinkle half of it with about 1/2 cup of the cheese mixture and 1/4 cup of the shredded chicken. Drizzle with a tablespoon of the sauce. Fold the tortilla in half.
Heat the remaining 1 tablespoon of Olive oil in the skillet over medium heat. Cook the quesadilla for 3-4 minutes per side, or until golden brown and the cheese is melted.
Repeat with the remaining tortillas, cheese, chicken, and sauce. Serve immediately with extra sauce on the side.