Remove the husks and silk off 1 ear of corn. Laying the corn flat on a cutting board, cut one side of the kernels off the cob. Keep rotating the ear of corn so that there is a flat side on the cutting board. Cut the kernels off a side each time you rotate the ear.
Remove the husks off the tomatillos and rinse to remove the sticky residue.
Remove the core from the top of the tomatillo. Slice each tomatillo in half laterally so that you have two wide pieces.
Slice the onion into thin slivers.
Remove the zest from the lime with the Microplane or the smallest holes on a box grater.
Mince the garlic.
Salt and pepper the chicken thighs.
Place the cast iron skillet over medium-high heat.
Once the skillet feels hot, add olive oil.
When the oil is hot, add the tomatillos and the jalapeno pepper to the skillet. Let them start to char for about 4 minutes.
Flip the tomatillos over and push them to one side of the pan. They should be blackened in spots. Rotate the pepper. Add the onion and the corn.
Keep stirring the corn and onions as they start to brown. Check the tomatillos. If they are getting very charred, flip them over again. Check the jalapeno pepper as well. If it looks blackened, remove it and place it to the side.
After the corn and onions have been cooked for 7 minutes, they should be browned. Remove the vegetables from the pan and onto a plate.
Add another teaspoon of olive oil to the pan.
Once the oil is hot, add the chicken thighs. Let them sear for 3 minutes.
Flip the chicken over and sear the other side for 3-4 minutes.
Dice the jalapeno while the chicken is searing.
Add the vegetables back to the pan and turn the heat down to medium. Cover the pan for 5 minutes. The chicken should be fully cooked now.
Add the garlic, jalapeno pepper, lime zest, and the juice of one lime to the pan.
With a metal spatula, start to break the chicken into pieces and mash the tomatillos. You want the chicken to be in small bite-sized pieces. The filling will start to meld together as everything is mashed.
Add 2 tablespoons of chopped cilantro, ½ teaspoon of kosher salt, and ¼ teaspoon of ground black pepper.
Remove the skillet from the heat.
Coat a nonstick pan with cooking spray and place over medium heat. Lay a flour tortilla in the pan.
Add ¼ cup of cheese to one side of the tortilla. Scoop ½ cup of the filling on top of the cheese.
Add another ¼ cup of cheese on top of the filling. Fold the tortilla over the filling, pressing down slightly to make sure it stays.
After 2-3 minutes, check the underside of the quesadilla to see if the tortilla is browned. If it is, carefully flip the quesadilla over. Cook for 2 minutes until the bottom has been browned.
Remove the quesadilla from the pan and cut it in half to serve.