This paper introduces a novel deployable reflector concept which achieves single degree-of-freedom folding of solid doubly curved surfaces. A set of folding kinematics is constructed using the Miura–Ori pattern and the Hoberman linkage to allow compact collision-free stowage of a fully rigid truss-supported solid-surface reflector structure. In this paper, the baseline kinematic architecture is introduced, and a design methodology using Bayesian optimization to systematically obtain optimally stowed geometries is detailed. An example design is carried out to demonstrate the methodology. Optimal parameters are produced, the design space is explored, and a detailed design based on the optimal parameters is made, along with its derivative variants. Finally, a prototype model and quantification of surface errors confirm the validity of resulting designs.