This article proposes a novel optimal hybrid control framework to improve the voltage profile of highly unbalanced Distribution Grids (DGs) by coordinating the injection of reactive power from multiple off-board Electrical Vehicles (EVs) chargers. It exploits the time-synchronized measurements advantages, centralized control, and local controllers embedded into a hierarchical and scalable scheme, coordinated by the distribution system operator (DSO). The proposed framework is aimed to increase the modern electrical networks' flexibility, reliability, and stability. It is powered by the Eigensystem Realization (ER)-based system identification technique, a Linear Quadratic Gaussian (LQG) controller, the Distribution-level Phasor Measurement Units (D-PMUs), and a new aggregator agent that handles the EV chargers power injection to precisely and timely regulate the dynamic voltage response in a sub-area or the entire DG. The robustness and feasibility of the proposal are demonstrated by employing simulated scenarios with unbalanced faults, latency in communications, and highly unbalanced loads conditions on the IEEE 13 and 123 nodes test feeders, compensating the voltage variations accurately in less than 205 ms. The promising outcome of this study suggests a novel application for an emerging measurement-based control system in the operation of modern active DGs.