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Hybrid organic-inorganic perovskites are semiconductors that have great potential for optoelectronic applications such as light-emitting diodes, photodetectors, and solar cells. In such devices, the surface plays a crucial role in the performance and stability, as it strongly influences the recombination rate of excited charge carriers. It is reported that molecular ligands such as benzylamine are capable of reducing the surface trap state density in thin films. In this work, we aim to clarify the mechanisms that govern the surface passivation of hybrid perovskites by benzylamine. We developed a versatile approach to investigate the influence of benzylamine passivation on the well-defined surface of freshly cleaved hybrid perovskite crystals. We show that benzylamine permanently passivates surface trap states in these single crystals, resulting in enhanced photoluminescence and charge carrier lifetimes. Additionally, we show that exposure to benzylamine leads to the replacement of the methylammonium cations by benzylammonium, thereby creating a thermodynamically more stable two-dimensional (2D) perovskite (BA)2PbBr4 on the surface of the three-dimensional crystal. This conversion to a 2D perovskite drives an anisotropic etching of the crystal surface, with the {100} planes being most prone to etching. Initially, square etching pits appear spread over the surface. As time elapses, these etching pits broaden and merge to yield large flat terraces that are oriented normally to the cleaving plane when they form. A thorough understanding of the mechanisms governing the surface passivation is crucially important to optimize and design novel passivation schemes, with the ultimate goal of further advancing the efficiency of optoelectronic devices based on hybrid perovskites.