Aiming to take full advantage of Electric Vehicles' (EVs) batteries, this paper proposes a two-level hierarchical model predictive controller coupled with an innovative charging-discharging scheduler for EVs in Building Microgrids (BMGs). This paper provides a complete framework for the design of this control structure and analyses its performance regarding the state of charge of the EVs at departure time, the self-consumption rate, and the coverage rate, considering a residential BMG equipped with photovoltaic panels and static Li-ion batteries. The results and performance of the proposed control architecture are compared to two other solutions: a hierarchical predictive controller with no scheduler and a rule-based algorithm. A technological and economical study is also performed considering variables such as the dimension of the EV's park, the price of energy, the cost of maintenance, the possibility to discharge or not into the grid, and the execution time of the control architecture. The simulation results conducted in MATLAB Simulink demonstrated that the proposed control structure ensures the full charging of all vehicles at departure time while also improving the self-consumption rate of the BMG with a relatively low stress on the needed computation capacities, even when considering a large fleet of vehicles.Read less <