We consider a general electric vehicle (EV) charging system with stochastic demand, demand request locations, and predetermined charging facilities (including charging station locations and charger capacities). The objective is to design a good routing strategy that accommodates well demand-request dynamics so as to satisfy the charging system’s stability constraints and also minimize the EV’s mean response time. We introduce a class of flexible and measurement-based routing policies called “partition-based random routing” (PBRR) and show that the performance measure of interest can be formulated as a constrained optimization problem with a convex objective function when the system is heavily loaded. This formulation enables us to establish strong theoretical results that are in aid of finding the optimal routing solution; however, in practice, finding this solution requires rather involved numerical calculations. To that end, we propose a surrogate, easy to design and implement, optimization algorithm for finding the desired optimal routing solution. Numerical work based on synthetic data shows that the performance of the developed routing strategy and its fast implementation is highly satisfactory for a number of system settings.