Sustainable and scalable electrolytic aqua hydrogen technology is expected to establish hydrogen energy as an effective alternative to traditional fossil fuels. The rational design and development of highly active electrocatalysts for the hydrogen evolution reaction (HER) are crucial for advancing water-splitting technologies. In this work, we synthesized the MOF-199 framework material (C–Cu) through high-temperature hydrothermal preparation followed by carbonization. The C–Cu@Pd composite materials were prepared using two different methods: galvanic replacement reaction (GRR) and electrochemical cyclic voltammetry (EC). The microstructure, morphology, elemental distribution, surface electronic states, and electrocatalytic performance of the composite materials were comprehensively investigated and analyzed using transmission electron microscopy (TEM), scanning electron microscopy (SEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), energy-dispersive X-ray spectroscopy (EDS), linear sweep voltammetry (LSV), electrochemical impedance spectroscopy (EIS), and current-time (i–t) curves. The results revealed that, compared to C–Cu@Pd(GRR), the C–Cu@Pd(EC) catalyst demonstrated superior HER performance, characterized by a small overpotential of 91.0 mV at 10.0 mA·cm–2 and a Tafel slope of 56.0 mV·dec–1. Furthermore, the C–Cu@Pd(EC) catalyst exhibited exceptional long-term stability during a 4000-cycle cyclic voltammetry (CV) stability test. The outstanding performance of C–Cu@Pd(EC) was attributed to the synergistic effect of the CuPd alloying phase, which facilitates electron transfer to the electrocatalyst surface and enhances the electrochemical activity of the catalyst.