This paper presents models and optimization methods for the design of electric vehicle propulsion systems. Specifically, we first derive a bi-convex model of a battery electric powertrain including the transmission and explicitly accounting for the impact of its components' size on the energy consumption of the vehicle. Second, we formulate the energy-optimal sizing and control problem for a given driving cycle and solve it as a sequence of second-order conic programs. Finally, we present a real-world case study for heavy-duty electric trucks, comparing a single-gear transmission with a continuously variable transmission (CVT), and validate our approach with respect to state-of-the-art particle swarm optimization algorithms. Our results sho...