Electric vehicle (EV) charging stations are increasingly operated with an aggregate power limit below the sum of their port ratings, and require scheduling algorithms to divide the available power among the connected EVs. Charging standards permit a current that is either zero or at least a minimum rate, typically 6 A, which makes this allocation problem non-convex. Existing methods either solve a mixed-integer program with a commercial solver, which can be computationally expensive, adds software dependencies, and incurs licensing costs, or apply heuristics without optimality guarantees. This paper proposes Bisect-Index-Choose (BIC), a fast and solver-free scheduling algorithm that computes a globally optimal allocation among EVs under mild assumptions on their utilities. For $n$ EVs, BIC runs in $O(n \log n)$ time when all EVs share one maximum rate and in $O(n^2)$ time for two, times a logarithmic factor in the numerical precision. In tests with up to 1000 EVs, BIC attains global optimality and is up to three orders of magnitude faster than the solver. On real-world charging data, it needs less capacity and delivers more energy than existing heuristics. We implement BIC on a low-cost microcontroller and show that it solves instances with 1000 EVs in less than 90 ms.