Lightly butter one side of each tortilla. Place one tortilla in a hot skillet over medium-high heat. Layer half of the cheese, chicken, peppers, and onions on the tortilla. Top with the remaining cheese. Place the second tortilla on top and cook for a minute or two.
When the cheese is melting and the tortilla facing the skillet begins to brown, use a large spatula to carefully flip the tortilla over and cook on the second side for a few minutes.
When everything has melted together and the tortillas are golden and crisp, remove the quesadilla from the skillet and slice it into wedges. Serve warm.
Notes
Mozzarella, cheddar, Colby jack, and Pepper jack cheeses will all work well in this recipe.