A key challenge in contact-rich dexterous manipulation is the need to jointly reason over global geometry and nonsmooth contact dynamics. End-to-end policies bypass this complexity, but often require large amounts of data and transfer poorly from simulation to reality. We address the limitations with a simple insight: dexterous manipulation is inherently hierarchical--at a high level, a robot decides where to touch (geometry); at a low level it determines how to move the object through contact dynamics. Building on this insight, we propose a hierarchical RL--MPC framework in which a high-level reinforcement learning (RL) policy predicts a contact intention, a novel object-centric interface that specifies (i) an object-surface contact location and (ii) a post-contact object subgoal pose. Conditioned on the contact intention, a low-level contact-implicit model predictive control (MPC) optimizes local contact modes and real-time (re)plans through contact dynamics to generate robot actions that robustly move the object toward each subgoal. We evaluate the framework on non-prehensile tasks, including geometry-generalized pushing across diverse object shapes, pivoting/flipping-based object reorientation, and environment-assisted object repositioning. It achieves high success rate with substantially reduced data (10 times less than end-to-end baselines), highly robust performance, and zero-shot sim-to-real transfer.