Warm the skillet over medium heat and lightly brush with oil. Fold the tortillas in half to create small sandwiches and place them in the skillet.
Sprinkle shredded chicken evenly over half of each tortilla, then top with shredded cheese. Fold the tortillas closed if they aren't already folded.
Cook the quesadillas for about 2-3 minutes on each side, pressing gently with a spatula, until the outside is golden brown and crispy, and the cheese inside is melted.
Carefully flip the quesadillas with a spatula to ensure even browning on both sides. Listen for a gentle sizzling and watch for a crispy crust forming.
Once golden and crispy, remove the quesadillas from the skillet and let them rest for a minute or two, allowing the cheese to settle and cool slightly.
Cut the quesadillas into halves or quarters and serve hot for a crispy, cheesy treat.
