A new cobalt metal-organic framework (2D-Co-MOF) based on well-defined layered double cores that are strongly connected by intermolecular bonds has been developed. Its 3D structure is held together by π-π stacking interactions between the labile pyridine ligands of the nanosheets. In aqueous solution, the axial pyridine ligands are exchanged by water molecules, producing a delamination of the material, where the individual double nanosheets preserve their structure. The original 3D layered structure can be restored by a solvothermal process with pyridine, so that the material shows a "memory effect" during the delamination-pillarization process. Electrochemical activation of a 2D-Co-MOF@Nafion-modified graphite electrode in aqueous solution improves the ionic migration and electron transfer across the film and promotes the formation of the electrocatalytically active cobalt species for the oxygen evolution reaction (OER). The so-activated 2D-Co-MOF@Nafion composite exhibits an outstanding electrocatalytic performance for the OER at neutral pH, with a TOF value (0.034 s-1 at an overpotential of 400 mV) and robustness superior to those reported for similar electrocatalysts under similar conditions. The particular topology of the delaminated nanosheets, with quite distant cobalt centers, precludes the direct coupling between the electrocatalytically active centers of the same sheet. On the other hand, the increase in ionic migration across the film during the electrochemical activation stage rules out the intersheet coupling between active cobalt centers, as this scenario would impair electrolyte permeation. Altogether, the most plausible mechanism for the O-O bond formation is the water nucleophilic attack to single Co(IV)-oxo or Co(III)-oxyl centers. Its high electrochemical efficiency suggests that the presence of nitrogen-containing aromatic equatorial ligands facilitates the water nucleophilic attack, as in the case of the highly efficient cobalt porphyrins.