A brushless doubly-fed machine (BDFM) is an attractive option for megawatt-scale turbo-electric propulsion systems due to use of a partially-rated power converter, reduced maintenance, and absence of permanent magnets. However, the BDFM has inherently poor torque density because of machine saturation, even at low current-density, that offsets all the benefits. This paper proposes an approach to maximize the torque density by finding appropriate electrical excitations on the two stator windings for a given machine dimension while remaining within flux- and current-density limits. A single-objective optimization problem is formulated. The obtained results prove that while designs with equal electrical loadings on both stators, and an initial current phase offset of π/2 between the two stators, may seem a good design approach, they are far from being optimal. Our optimized solution establishes that the phase offset of 2π/3 provides maximum torque capability for an identical dimension. This procedure is validated using FEA simulations. Operating with this design also leads to higher machine efficiency and better power factor on the secondary stator, thus reducing the converter rating.