Combine shredded chicken, Greek yogurt, Laughing Cow cheese wedge, shredded mozzarella, and ranch seasoning in a medium bowl. Mix with a fork until completely smooth and creamy with no visible lumps. If the Laughing Cow is too firm straight from the fridge, microwave the bowl for 10 seconds to soften before mixing. Do not skip this step or the filling will not blend smoothly.

Lay the tortilla flat on a clean cutting board. Spoon the chicken filling onto one half and spread evenly about 1/4-inch thick, leaving a small border around the edge. Fold the empty half over the filling to form a half-moon shape and press the edges lightly to seal.

Place a 10-inch non-stick skillet over medium heat. Add the butter and let it melt completely, swirling to coat the pan evenly. Wait until the butter is sizzling and fragrant before adding the quesadilla. Adding it too early causes steaming rather than crisping.

Place the folded quesadilla in the center of the pan. Cook for 2 to 3 minutes on the first side until the bottom is deep golden brown and crispy. Flip carefully using a wide spatula and cook for another 2 to 3 minutes until the second side is evenly golden. Total cook time is about 4 to 6 minutes.

Transfer to a cutting board and let rest for 1 full minute before slicing. This keeps the filling from spilling out. Slice into three triangles and serve immediately.