Personal devices have adopted diverse authentication methods, including biometric recognition and passcodes. In contrast, headphones have limited input mechanisms, depending solely on the authentication of connected devices. We present Moonwalk, a novel method for passive user recognition utilizing the built-in headphone accelerometer. Our approach centers on gait recognition; enabling users to establish their identity simply by walking for a brief interval, despite the sensor's placement away from the feet. We employ self-supervised metric learning to train a model that yields a highly discriminative representation of a user's 3D acceleration, with no retraining required. We tested our method in a study involving 50 participants, achieving an average F1 score of 92.9% and equal error rate of 2.3%. We extend our evaluation by assessing performance under various conditions (e.g. shoe types and surfaces). We discuss the opportunities and challenges these variations introduce and propose new directions for advancing passive authentication for wearable devices.