This paper presents a comprehensive control of modular multilevel converter-based high-voltage direct current (MMC-HVDC) integrated offshore wind farm (OWF) system, which is aimed at enhancing the fast frequency support capability. The comprehensive control consists of the active energy control (AEC), the optimized energy control (OEC), and the OWF control. The proposed OEC decouples the voltage of MMC submodule (SM) capacitor and the DC-link voltage of the MMC-HVDC. A mathematical model of the energy release process in an MMC and onshore frequency dynamics is developed, and a sinusoidal-function-based energy utilization preset curve is derived to theoretically achieve optimized frequency support, while ensuring the constrained energy usage. Upon the occurrence of a frequency event, MMC SMs may adjust their responses according to the energy utilization preset curve. The MMC then provides onshore frequency support by releasing energy. The coordination process with the OWF is also explored to further enhance the frequency support performance. Finally, case studies are conducted on the PSCAD/EMTDC platform through employing actual engineering parameters. The frequency support performance of various controls under both load increase and load decrease conditions are compared, demonstrating the effectiveness of the proposed OEC.