Complex cell shapes are generated first by breaking symmetry, and subsequent polar growth. Localized bending of anticlinal walls initiates lobe formation in the epidermal pavement cells of cotyledons and leaves, but how the microtubule cytoskeleton mediates local cell growth, and how plant pavement cells benefit from adopting jigsaw puzzle-like shapes, are poorly understood. In Arabidopsis (Arabidopsis thaliana), the basic Pro-rich protein (BPP) microtubule-associated protein family comprises seven members. We analyzed lobe morphogenesis in cotyledon pavement cells of a BPP1;BPP2;BPP5 triple knockout mutant. New image analysis methods (MtCurv and BQuant) showed that anticlinal microtubule bundles were significantly reduced and cortical microtubules that fan out radially across the periclinal wall did not enrich at the convex side of developing lobes. Despite these microtubule defects, new lobes were initiated at the same frequency as in wild-type cells, but they did not expand into well-defined protrusions. Eventually, mutant cells formed nearly polygonal shapes and adopted concentric microtubule patterns. The mutant periclinal cell wall bulged outward. The radius of the calculated inscribed circle of the pavement cells, a proposed proxy for maximal stress in the cell wall, was consistently larger in the mutant cells during cotyledon development, and correlated with an increase in cell height. These bpp mutant phenotypes provide genetic and cell biological evidence that initiation and growth of lobes are distinct morphogenetic processes, and that interdigitated cell geometry effectively suppresses large outward bulging of pavement cells.