Toss the chicken. In a medium bowl, mix the shredded chicken with buffalo sauce until fully coated. Set aside.
Prep your tortillas. Lay out your tortillas on a flat surface. Spread a thin layer of ranch dressing over one half of each tortilla.
Layer it up. Evenly distribute the buffalo chicken over the ranch side of each tortilla, then top with both cheeses. Fold the empty half of the tortilla over the filling.
Cook the quesadillas. Melt ½ tablespoon of butter in a large skillet over medium heat. Place one folded quesadilla in the pan and cook for 3–4 minutes per side, until golden brown and the cheese is fully melted. Repeat with remaining quesadillas, adding butter between each one.
Slice and serve. Let each quesadilla rest for one minute before slicing into three wedges. Serve immediately with your favorite dippers.