Inhomogeneous in-plane deformation of soft materials or cutting and folding of inextensible flat sheets enables shape-morphing from two dimensional (2D) to three-dimensional (3D), while the resulting structures often have weakened mechanical strength. Shells like nacre are known for the superior fracture toughness due to the "brick and mortar" composite layers, enabling stress redistribution and crack stopping. Here, we report an optimal and universal cutting and stacking strategy that transforms composite plies into 3D doubly curved shapes with nacre-like architectures. The multilayered laminate exhibits staggered cut distributions, while the interlaminar shear mitigates the cut-induced mechanical weakness. The experimentally consolidated hemispherical shells exhibit, on average, 37 and 69% increases of compression peak forces, versus those with random cut distributions, when compressed in different directions. Our approach opens a previously unidentified paradigm for shape-conforming arbitrarily curved surfaces while achieving high mechanical performance.