Boosting nonlinear frequency conversion in extremely confined volumes remains a key challenge in nano-optics, nanomedicine, photocatalysis, and background-free biosensing. To this aim, field enhancements in plasmonic nanostructures are often exploited to effectively compensate for the lack of phase-matching at the nanoscale. Second harmonic generation (SHG) is, however, strongly quenched by the high degree of symmetry in plasmonic materials at the atomic scale and in nanoantenna designs. Here, we devise a plasmonic nanoantenna lacking axial symmetry, which exhibits spatial and frequency mode overlap at both the excitation and the SHG wavelengths. The effective combination of these features in a single device allows obtaining unprecedented SHG conversion efficiency. Our results shed new light on the optimization of SHG at the nanoscale, paving the way to new classes of nanoscale coherent light sources and molecular sensing devices based on nonlinear plasmonic platforms.