Charged particle velocity-space diffusion in a prescribed one-dimensional turbulent electric field is investigated through numerical trajectories in phase-space and compared against quasi-linear theory (QL), including resonance broadening (RB). A Gaussian spectrum electric field of variable amplitude E is studied in conjunction with two plasma dispersion relations, namely, the Langmuir and ion-acoustic dispersion. A first parameter scan shows that RB effects become significant for a Kubo number K of a few percent. A Kubo number scan shows that diffusion increases as a power law of D∝K3∝E3/2 for large Kubo numbers. Moreover, at large Kubo numbers, transport processes include significant diffusion measured at velocities much higher than the resonant region, where QL and RB predict negligible diffusion. For times much larger than the trapped particle flight time τb and the autocorrelation time τ0, the velocity distribution departs from a Gaussian. Nevertheless, measurements show that the variance increases linearly in time, with a Hurst parameter of H∼0.5, where the diffusion scales as K5/2∝E5/4 and K3/2∝E3/4 for small and large Kubo number, respectively.