Decades of in-situ observations of whistler-mode waves in Earth's magnetosphere reveal that there is frequently a gap in the spectral power at around half the local electron gyrofrequency. Recent theoretical and kinetic simulation studies have suggested that the gap arises due to the presence of temperature anisotropy in both a ``warm' and a ``hot' electron population, leading to two separate (and independent) regions of wave growth in frequency space. We present two-dimensional kinetic plasma simulations using the powerful EPOCH particle-in-cell code that offer an alternative explanation. After an initial linear-growth period, our simulations show self-consistent formation of a gap feature. In most cases this arises where linear theory predicts the maximum growth rate, and is associated with subtle local structuring of the hot electron distributions. This feature persists in multiple simulations with varying hot electron parameters. We discuss these results in the context of in-situ observations of both waves and electron distribution functions and argue that the rapid reorganisation of electron distributions in a small, but key, region of phase-space during the growth of whistler-mode waves naturally results in the spectral gap often observed at half the electron gyrofrequency.