Boosting nonlinear frequency conversion in extremely confined volumes remains a challenge in nano-optics research(1), but can enable applications in nanomedicine(2), photocatalysis(3) and background-free biosensing(4). To obtain brighter nonlinear nanoscale sources, approaches that enhance the electromagnetic field intensity and counter the lack of phase matching in nanoplasmonic systems are often employed(5-8). However, the high degree of symmetry in the crystalline structure of plasmonic materials (metals in particular) and in nanoantenna designs strongly quenches second harmonic generation(5). Here, we describe doubly-resonant single-crystalline gold nanostructures with no axial symmetry(9) displaying spatial mode overlap at both the excitation and second harmonic wavelengths. The combination of these features allows the attainment of a nonlinear coefficient for second harmonic generation of similar to 5 x 10(-10) W-1, enabling a second harmonic photon yield higher than 3 x 10(6) photons per second. Theoretical estimations point toward the use of our nonlinear plasmonic nanoantennas as efficient platforms for label-free molecular sensing.