A new path for the generation of a sub-ion-scale cascade in collisionless space and astrophysical plasma turbulence, triggered by magnetic reconnection, is uncovered by means of high-resolution two-dimensional hybrid-kinetic simulations employing two complementary approaches, Lagrangian and Eulerian, and different driving mechanisms. The simulation results provide clear numerical evidence that the development of power-law energy spectra below the so-called ion break occurs as soon as the first magnetic reconnection events take place, regardless of the actual state of the turbulent cascade at MHD scales. In both simulations, the reconnection-mediated small-scale energy spectrum of parallel magnetic fluctuations exhibits a very stable spectral slope of $\sim -2.8$, whether or not a large-scale turbulent cascade has already fully developed. Once a quasi-stationary turbulent state is achieved, the spectrum of the total magnetic fluctuations settles toward a spectral index of $-5/3$ in the MHD range and of $\sim -3$ at sub-ion scales.