Passive Optical Network (PON) elements such as Optical Line Terminal (OLT) and Optical Network Units (ONUs) are currently managed by legacy, non-flexible network management systems. Software-Defined Networking (SDN) is a new networking paradigm that improves the operation and management of networks. In this paper, we propose a novel architecture, based on the SDN concept, for Ethernet Passive Optical Networks (EPON) that includes the Service Interoperability (SIEPON) standard. In our proposal the OLT is partially virtualized and some of its functionalities are allocated to the core network management system, while the OLT itself is replaced by an OpenFlow (OF) switch. A new MultiPoint MAC Control sublayer extension based on the OpenFlow protocol is presented. The controller is designed to effectively manage and enhance the resource utilization, flow monitoring, bandwidth assignment, quality-of-service (QoS) guarantees, and energy management of the optical network access. The OpenFlow switch is extended with synchronous ports to keep the time-critical nature of the EPON network. OpenFlow messages are also extended with new functionalities to implement the concept of EPON Service Paths (ESPs). Our simulation-based results demonstrate the effectiveness of the new architecture, while keeping similar or improved performance compared to legacy PONs, in terms of delay and throughput.