In a medium bowl, combine all of the chicken mixture ingredients, stir to combine and set aside.
In a small bowl, combine the sour cream/Greek yogurt ingredients. Set aside until ready to use.
Lay 4 tortillas on a flat surface. Evenly divide the pepper jack cheese onto each tortilla. Evenly divide the chicken mixture between the 4 tortillas. Top with the Monterrey jack cheese. Place the remaining 4 tortillas on top of each prepared tortilla.
Preheat a flat-top griddle or skillet over medium heat. Brush skillet with oil. Place one (or more if you have a large cook-top) quesadilla onto the skillet. Cook over medium for about 5-7 minutes or until brown and crispy. Flip and cook for another 3-5 minutes until brown and crispy. Repeat with remaining quesadillas.
Slice into 4 triangles and serve with chipotle sour cream and fixings.
I use rotisserie chicken in this recipe, it works perfect. The chipotles in adobo add a good amount of heat/spice. If you are unsure about the heat level or are making for kids you can dial the measurements back.
You could use larger tortillas but your fillings will just not go as far. I highly recommend using flour tortillas. I just love how crispy they get, and you don't get that with "diet" tortillas.
I like my quesadillas pretty thin, and not overly filled with cheese where they become sloppy and soggy, but you can certainly add as much cheese as you please!