Designing healthier lipids is a current approach to developing potential functional foods. Olive pomace oil (OPO) has beneficial effects on human health, attributed to its high oleic acid content and unique bioactive compounds. Four puff pastry margarines (PP-M), based on OPO (M1, M2 at 40.8%, and M3, M4 at 30.8%, and cocoa butter at 10%) combined with low molecular weight organogelators, were prepared using two initial cooling rates (M1, M3 at 0.144 °C/min and M2, M4 at 0.380 °C/min) and compared to both commercial puff pastry (PP) butter (CB) and fatty preparation (CFP). Subsequently, six baked PP counterparts were elaborated. Physical-chemical, mechanical properties, and lipid profiles were analyzed in M1–M4 and PP, while thermal properties were determined in M1–M4. Sensory analysis was carried out in PP-M1 and PP-M3 counterparts. Elasticity (G′) of M1–M4 samples was between that of controls CB and CFP, although a higher OPO content reduced viscous modulus (G″). The initial cooling rate did not affect the melting behavior of M1–M4. The firmness of PP-M1 was similar to that of PP-CB and PP-CFP, and the better spreadability and plasticity of M1 positively favored PP puffing. In addition, PP-M1 had 36.8% less SFA content than baked PP-CB, and its overall acceptability was similar. For the first time, a new margarine with high OPO content, showing adequate firmness, spreadability, and plasticity, was formulated, which gave rise to PP with appropriate performance and sensory quality and a healthy lipid profile.