Preheat the oven to 200°F and set a baking sheet in the oven. Heat the olive oil in a large skillet over medium heat. Add the onion and bell pepper and cook for 4 to 5 minutes, or until softened.
Add the shredded chicken, green chiles, taco seasoning, and salsa. Stir until the chicken is evenly coated and heated through. If the mixture seems dry, add a bit of water. Remove from the heat.
Melt about ½ tablespoon butter in a large skillet or on a griddle over medium heat. Place a tortilla in the skillet. Sprinkle a handful of cheese over the entire tortilla. Cook for 30 to 60 seconds, or until the cheese begins to melt.
Spread a generous ⅓ cup of the chicken filling over one half of the tortilla, then fold the other half over the filling. Cook for 2 to 3 minutes per side, or until the tortilla is golden and crisp and the cheese is fully melted.
Transfer the cooked quesadilla to the warm baking sheet in the oven while you cook the remaining quesadillas. Repeat with the remaining tortillas, adding more butter to the skillet as needed.
Slice the quesadillas into wedges. Serve warm with salsa, sour cream, and guacamole.
Notes
Choose your chicken: Slow cooker shredded chicken works perfectly in this recipe, but rotisserie chicken is an easy shortcut.For the best melt: Freshly shredded cheese melts more smoothly than pre-shredded cheese.Cook over medium heat: This gives the tortillas time to crisp up without burning before the cheese melts.Keep batches warm: Place finished quesadillas on a baking sheet in a 200°F oven while you cook the rest.Storage and reheating: Store leftover quesadillas in the refrigerator for up to 3 days. Reheat them in a skillet over medium-low heat or in a 350°F oven until warmed through and the tortillas are crisp again. Skip the microwave if you can; it warms them quickly, but it also softens the tortillas.