In a proton-electron magnetized plasma, we analyze turbulence at kinetic scales captured by a gyrokinetic formalism. The interval of scales spans the range between the proton and the electron gyroradii, while the use of the proper mass ratio between the two species ensures a realistic scale separation for the nonlinear couplings. The simulation is pertinent to astrophysical conditions, employing a straight field line magnetic geometry for the guide field, a plasma $\beta$ of one and a temperature ratio between the two species of unity. We investigate the intermittency of the distribution functions in the perpendicular direction, measured over the phase space as a way to account for the velocity space structures generated via Landau damping as well as for the nonlinear spatial mixing (i.e. the turbulent cascade). The analysis makes use of a Hermite decomposition in the parallel velocity. Electron structures are found to be strongly intermittent compared to weakly intermittent protons. Moreover, we find evidence linking intermittency with phase mixing and electron Landau damping, as intermittent electron structures also exhibiting strong parallel velocity structures.