Vehicle-to-building (V2B) systems integrate physical infrastructures, such as smart buildings and electric vehicles (EVs) connected to chargers at the building, with digital control mechanisms to manage energy use. By utilizing EVs as flexible energy reservoirs, buildings can dynamically charge and discharge them to optimize energy use and cut costs under time-variable pricing and demand charge policies. This setup leads to the V2B optimization problem, where buildings coordinate EV charging and discharging to minimize total electricity costs while meeting users' charging requirements. However, the V2B optimization problem is challenging because of: (1) fluctuating electricity pricing, which includes both energy charges ($/kWh) and demand charges ($/kW); (2) long planning horizons (typically over 30 days); (3) heterogeneous chargers with varying charging rates, controllability, and directionality (i.e., unidirectional or bidirectional); and (4) user-specific battery levels at departure to ensure user requirements are met. In contrast to existing approaches that often model this setting as a single-shot combinatorial optimization problem, we highlight critical limitations in prior work and instead model the V2B optimization problem as a Markov decision process (MDP), i.e., a stochastic control process. Solving the resulting MDP is challenging due to the large state and action spaces. To address the challenges of the large state space, we leverage online search, and we counter the action space by using domain-specific heuristics to prune unpromising actions. We validate our approach in collaboration with Nissan Advanced Technology Center - Silicon Valley. Using data from their EV testbed, we show that the proposed framework significantly outperforms state-of-the-art methods.