A fundamental challenge in teaching robots is to provide an effective interface for human teachers to demonstrate useful skills to a robot. This challenge is exacerbated in dexterous manipulation, where teaching high-dimensional, contact-rich behaviors often require esoteric teleoperation tools. In this work, we present HOLO-DEX, a framework for dexterous manipulation that places a teacher in an immersive mixed reality through commodity VR headsets. The high-fidelity hand pose estimator onboard the headset is used to teleoperate the robot and collect demonstrations for a variety of general purpose dexterous tasks. Given these demonstrations, we use powerful feature learning combined with non-parametric imitation to train dexterous skills. Our experiments on six common dexterous tasks, including in-hand rotation, spinning, and bottle opening, indicate that HOLO-DEX can both collect high-quality demonstration data and train skills in a matter of hours. Finally, we find that our trained skills can exhibit generalization on objects not seen in training. Videos of HOLO-DEX are available in the project URL.