Place cooked chicken into a medium-sized mixing bowl then set aside. In a separate bowl, stir together melted butter and pepper sauce until completely combined. Pour sauce over cubed chicken then stir until chicken is coated completely in the sauce. Set aside.
Place a large non-stick skillet or grill pan over medium-low heat then let a few seconds pass so skillet can come to temperature. Coat surface lightly with cooking spray. Alternatively, you can brush a light amount of butter into the pan. Place a flour tortilla into the skillet then immediately add ½ cup shredded cheese to cover one-half of the tortilla. Spread 1/2 cup buffalo chicken on top of the cheese then fold the uncovered half of tortilla on top of the chicken and cheese.
Press down on the quesadilla using a spatula to force cheese and chicken into contact with heat, sealing the top and bottom together. Let tortilla cook on the first side for 2–3 minutes, until golden brown and crispy.
Flip quesadilla then cook for 2–3 minutes until golden brown and crispy on the opposite side. If the tortilla becomes too brown before the cheese melts, lower the temperature. The objective is for the cheese to be completely melted and gooey while at the same time becoming golden and crispy. Generally, if you have the patience for it, lower heat is better.
Transfer quesadilla to a cutting board, cut into wedges then serve with plenty of ranch or blue cheese dressing for dipping. Enjoy!