We study an online centralized charging scheduling problem in which a residential aggregator must decide, in real time, when to charge dynamically arriving electric vehicles (EVs) under feeder capacity limits, with the goal of flattening the load profile over a day. To tackle the computational difficulty of this setting, we “gamify” the problem by representing each EV as a Tetris-like block that must be dropped within its arrival–departure window on a time–capacity grid, and we use this game both as a modeling tool and as a learning environment. On the optimization side, we implement a mixed-integer programming oracle with perfect future information and a rolling re-optimization policy; on the heuristic side, we design simple row-filling and threshold-based rules that place new blocks using only local information. On the learning side, we generate expert demonstrations from oracle solutions, train a convolutional image-to-movement policy by supervised learning, and then improve it with Dataset Aggregation (DAgger), which repeatedly corrects the policy on the states it actually visits. In a case study calibrated to a typical Hydro-Québec feeder in the Greater Montréal Area with around 200 Level-2 charging sessions per day, the DAgger-trained policy consistently outperforms heuristic and re-optimization baselines in terms of maximum–minimum load difference and RMSE, and the resulting reductions in peak EV demand translate into potential avoided distribution-capacity costs of tens of millions of CAD per year compared with uncoordinated “plug-in-to-charge” behavior.