This study evaluates the production of base oils for biolubricants using fatty acid methyl esters (FAMEs) derived from sunflower oil as the raw material. The production process involved the synthesis of oleochemical esters through a single-step alkaline transesterification reaction with a high-molecular-weight polyol, such as trimethylolpropane (TMP). To assess the effectiveness of the developed catalytic system in conducting the transesterification reactions and its impact on the properties of the final product, two types of alkaline catalysts were used. Specifically, the reactions were carried out using either Ca/TEA alkoxide or sodium methoxide as catalysts in various configurations and concentrations to determine the optimal catalyst concentration and reaction conditions. Sodium methoxide served as the commercial benchmark catalyst, while the Ca/TEA alkoxide was prepared in the laboratory. The optimal concentration of Ca/TEA was determined to be 3.0% wt. in the presence of iso-octane and 3.5% wt. under vacuum, while the corresponding concentrations of CH3ONa for both cases were determined to be 2.0% wt. The synthesized biolubricant esters exhibit remarkable performance characteristics, such as high kinematic viscosities and low pour points—ranging from 33–48 cSt at 40 °C, 7.68–10.03 cSt at 100 °C, to −14 to −7 °C, respectively—which are comparable to or improved over those of mineral oils such as SN-150 or SN-500, with the Ca/TEA alkoxide-catalyzed systems showing superior oxidation stability and reduced byproduct formation.