We propose a dynamic bandwidth allocation (DBA) scheme for EPON (Ethernet Passive Optical Network) Protocol over Coax, or EPoC in short. EPoC is the transparent extension of EPON over a cable operator's Hybrid Fiber-Coax (HFC) network, and is set to become a rapidly-evolving standard within the next few years, with strong backing from the industry, and with the creation of the IEEE 802.3bn Task Force. For managing and controlling EPoC, a network operator prefers to have a unified scheduling and quality-of-service (QoS) environment that includes both the optical and coax portions of the network. This is achieved by extending the EPON Medium Access Control (MAC) to run over the coax physical layer, to have a centralized end-to-end network control from the cable headend to the end-users' premises. In this paper, we describe a centralized DBA scheme for EPoC, where all allocation decisions are made at the operator's headend. The DBA is aware of the hybrid nature of the network, and considers round-trip times between optical and coax network units for intelligent and efficient allocations. We also formulate the allocation problem as a generalized optimization problem, which can be extended according to specific deployment scenarios. We present some initial simulation results to demonstrate the performance of the DBA.