In a mixing bowl, combine the sour cream, mayonnaise, McCormick taco seasoning, chili powder, and Tabasco green jalapeño sauce. Mix well until smooth and creamy. Taste and adjust the seasoning or heat level if necessary. Set aside.
Heat the extra virgin olive oil in a skillet over medium heat. Season the chicken breasts with salt and pepper. Add the chicken to the skillet and cook for about 6-7 minutes on each side or until fully cooked through and no longer pink in the center. Remove from the skillet and let it rest for a few minutes before slicing it into strips.
In a large skillet, place one tortilla and sprinkle half of the Monterey Jack and Cheddar cheese on one half of the tortilla. Layer the sliced chicken on top of the cheese, then add more cheese on top of the chicken. Fold the tortilla over to create a half-moon shape.
Cook the quesadilla in the skillet over medium heat for about 3-4 minutes on each side, or until the tortilla is golden brown and the cheese is melted. Repeat the process with the remaining tortillas.
Cut the quesadillas into wedges and serve them hot with the creamy jalapeño sauce for dipping. Enjoy your homemade Copycat Taco Bell Chicken Quesadilla with Creamy Jalapeño Sauce!