Pre cook your tortillas if they are not cooked already.
Make sure your chicken and peppers are ready to go. Use any leftover chicken, or bake some, and shred. Roast the peppers by placing them on the top shelf of the oven on the broil setting. Leave the oven door open just a crack. Roast on the heat until the peppers start to turn black and the skin is blistered. Rotate and repeat until all sides are roasted. This will take only a couple minutes per side. Remove the peppers from the oven and place in a sealed bag or tupperware to sweat (this makes them easier to peel). When cool enough to handle, scrape off the blistered skins and discard. Remove the stem and seeds from the peppers (they may tear and break, this is fine).
Heat a nonstick skillet over medium heat. Make sure all of your ingredients are ready to go as you will be building quickly in the skillet.
When everything is diced and ready, put the butter into the skillet. As soon as the butter is melted, placed a tortilla in the skillet.
Add 1/2 cup of the monterey jack cheese spread out on the tortilla in the skillet.
Lay slices of the roasted peppers across the entire tortilla in a single layer. Sprinkle the chicken, onion, corn, cumin, and cilantro on top. Add the remaining monterey jack cheese on top.
Place the remaining tortilla on top of it all and press down lightly.
Cover with a lid that at least reaches to the edge of the tortilla. This is to trap in the heat to help melt the cheese without overcooking the tortilla itself.
Cook for approximately 3-4 minutes until the tortilla is lightly browned. With a hand on top of the quesadilla, use a spatula to flip the quesadilla over. It should flip relatively easily as the melted cheese will hold things together and the toasted tortilla will be somewhat stiff and stay parallel to the skillet.
Cover the quesadilla again. Cook on the second side approximately 2-3 minutes until that side is also lightly browned and the cheese is melted. If the tortilla is browning too quickly, turn the heat down. If it is not browning fast enough, you can remove the cover to let out the steam and turn the heat up slightly. Exact results will vary based on your stove and skillet.
Remove the quesadilla and place on a cutting board to rest for 1-2 minutes. The resting will let the cheese start to settle so that it does not all leak out when cut.
Cut the quesadilla into triangles and serve with sour cream or your sauces of choice.