Minigolf, a game with countless court layouts, and complex ball motion, constitutes a compelling real-world testbed for the study of embodied intelligence. As it not only challenges spatial and kinodynamic reasoning but also requires reflective and corrective capacities to address erroneously designed courses. We introduce RoboGolf, a framework that perceives dual-camera visual inputs with nested VLM-empowered closed-loop control and reflective equilibrium loop. Extensive experiments demonstrate the effectiveness of RoboGolf on challenging minigolf courts including those that are impossible to finish.