Increased environmental and energy security concerns have made electric vehicles an attractive solution over the recent years. Therefore, improving their traction chain global efficiency, especially in high-speed region, became a major task in today's research. This paper investigates a novel optimization method applied on electric vehicles motorized by an Electrically Excited Synchronous Motor (EESM). The study proposes an algebraic method based on the Lagrange multiplier technique to control the motor torque efficiently while extending its speed limit using the additional degree of freedom offered by this type of machines. The reference currents are calculated offline and stored in lookup tables (LUT) using MATLAB/Simulink. The proposed method is compared to conventional Maximum Torque Per Ampere (MTPA) strategies applied on Internal Permanent Magnet Synchronous Machines (IPMSM) by maintaining the EESM excitation current constant and controlling the d-q axis currents for a likewise behavior. The optimization and speed limit extension benefits of the novel control scheme, especially in high-speed region, are emphasized via simulation results in the torque/speed domain.