For a creamier Buffalo wing sauce, stir together wing sauce and Ranch dressing in a medium size bowl. Or, leave out theRanch dressing for a more bold flavor. Add the green onions (optional) and shredded chicken.
Place a nonstick or cast iron skillet over medium to medium-low heat. Meanwhile, spread butter on one side of two tortillas and place one in the skillet, butter-side-down, as the skillet is heating up.
Quickly sprinkle 1/2 cup of cheese over the tortilla. Dollop 1 cup of the chicken mixture over the cheese and spread to the edges of the tortilla. Sprinkle another 1/2 cup of cheese over the chicken mixture and top with the other buttered tortilla, butter-side-up.
While the bottom tortilla is getting brown(about 1 to 2 minutes) and the cheese is starting to melt onto the bottom tortilla, spread butter on the remaining two tortillas.
When the bottom tortilla is golden brown, flip the quesadilla with a wide flat spatula.
Repeat the procedure with remaining tortillas and chicken mixture.
Cut quesadillas into 4 triangles. If desired, you can drizzle with additional Buffalo and Ranch dressing. Sprinkle with green onions, if you like!