This paper presents a novel modular, reconfigurable battery energy storage system. The proposed design is characterized by a tight integration of reconfigurable power switches and DC/DC converters. This characteristic enables isolation of faulty cells from the system and allows fine power control for individual cells toward optimal system-level performance. An optimal power management approach is developed to extensively exploit the merits of the proposed design. Based on receding-horizon convex optimization, this approach aims to minimize the total power losses in charging/discharging while allocating the power in line with each cell's condition to achieve state-of-charge (SoC) and temperature balancing. By appropriate design, the approach manages to regulate the power of a cell across its full SoC range and guarantees the feasibility of the optimization problem. We perform extensive simulations and further develop a lab-scale prototype to validate the proposed system design and power management approach.