The increasing demand for sustainable energy sources has positioned biodiesel as a viable alternative to fossil-derived fuels. This study investigates the use of hydrochar-based catalysts derived from garlic peel waste for biodiesel production via transesterification of vegetable oil. Hydrochar was synthesized through hydrothermal carbonization and applied as a heterogeneous catalyst. Process optimization was conducted using Response Surface Methodology (RSM) based on a Box–Behnken Design (BBD), evaluating the effects of methanol-to-oil ratio, catalyst concentration, reaction time, and temperature on fatty acid methyl ester (FAME) yield. Analysis of Variance (ANOVA) revealed that catalyst concentration was the most significant factor influencing FAME yield (p < 0.001), as further supported by the Pareto chart of standardized effects. The regression model demonstrated a good fit to the experimental data, with an R2 value of 83.79% and consistent adjusted and predicted R2 values. The maximum experimental FAME yield of 96.74% was achieved at a methanol-to-oil ratio of 6:1, catalyst loading of 3.0 wt%, reaction time of 1.5 h, and reaction temperature of 200 °C, while the RSM-predicted optimum yield was 88.08%. The produced biodiesel satisfied key EN 14214 physicochemical standards, including density, viscosity, flash point, and calorific value. Engine performance tests indicated favorable torque–load behavior at both low and high speeds, demonstrating suitability for small-scale engines and generators. However, reduced energy demand flexibility suggests limited applicability for heavy-duty engines, emphasizing the importance of application-specific fuel selection. Overall, garlic peel-derived hydrochar catalysts offer a sustainable and effective pathway for biodiesel production from renewable resources.