Eye-tracking plays a crucial role in the development of virtual reality devices, neuroscience research, and psychology. Despite its significance in numerous applications, achieving an accurate, robust, and fast eye-tracking solution remains a considerable challenge for current state-of-the-art methods. While existing reflection-based techniques (e.g., "glint tracking") are considered to be very accurate, their performance is limited by their reliance on sparse 3D surface data acquired solely from the cornea surface. In this paper, we rethink the way how specular reflections can be used for eye tracking: We propose a novel method for accurate and fast evaluation of the gaze direction that exploits teachings from single-shot phase-measuring-deflectometry(PMD). In contrast to state-of-the-art reflection-based methods, our method acquires dense 3D surface information of both cornea and sclera within only one single camera frame (single-shot). For a typical measurement, we acquire $>3000 \times$ more surface reflection points ("glints") than conventional methods. We show the feasibility of our approach with experimentally evaluated gaze errors on a realistic model eye below only $0.12^\circ$. Moreover, we demonstrate quantitative measurements on real human eyes in vivo, reaching accuracy values between only $0.46^\circ$ and $0.97^\circ$.