Begin by spreading the cooked and shredded pollo asado evenly over half of a tortilla, ensuring an even layer of flavorful meat.
Sprinkle a generous handful of shredded cheese over the pollo, covering it to let it melt into melty gooey goodness.
Fold the tortilla in half over the filling, pressing down gently to help it stay together.
Heat a skillet over medium heat and add a splash of vegetable oil, swirling to coat the surface.
Carefully place the folded quesadilla into the skillet, pressing down gently with a spatula, and cook for 3-4 minutes until the edges are golden brown and crispy.
Carefully flip the quesadilla using a spatula or tongs and cook for another 3-4 minutes until the second side is golden and cheese is melted inside.
Remove the quesadilla from the skillet and let it rest for a minute, then cut into quarters to reveal the gooey cheese and tender chicken inside.
Squeeze fresh lime juice over the hot quesadilla and serve immediately for maximum flavor and crunch.