The design of high-frequency transformers plays a pivotal role in electric vehicle charging systems, acting as the core component in isolated DC-DC converters. Achieving a transformer that not only operates well within the converter but also achieves high efficiency and compact size involves the balancing of numerous trade-offs. Managing the magnetic losses is essential as they dictate the efficiency but also govern the required transformer size for effective heat dissipation. This paper presents a novel transformer design method based on an exhaustive search algorithm that identifies the Pareto optimal transformers with minimised loss and weight. By introducing a Steinmetz equation filter, rapid computational speed and accuracy are combined. Loss estimations are based on experimentally validated analytical models, and the proposed methodology is experimentally validated by multiple transformer prototypes. Their operation in a dual active bridge is demonstrated by experimental measurements and circuit simulation. The results prove the effectiveness of the proposed design approach in achieving efficient and compact transformers.