Motivated by the recent Magnetospheric Multiscale (MMS) observations of oblique electron acoustic waves, we addressed the generation mechanism of the observed waves by utilizing the reductive perturbation technique. The nonlinear Zakharov-Kuznetsov (ZK) equation is derived for collisionless, magnetised plasma composed of cool inertial background electrons, the cool inertial electron beam, hot inertialess suprathermal electrons represented by a $\kappa$-distribution, and stationary ions. Moreover, the instability growth rate is derived by using the small-$k$ perturbation expansion method. Our findings reveal that the structure of the electrostatic wave profile is significantly influenced by the external magnetic field, the unperturbed hot, cool, and electron beam densities, the obliquity angle, and the rate of superthermality. Such parameters also affect the instability growth rate. This study clarifies the characteristics of the oblique electron solitary waves that may be responsible for changing the electron and ion distribution functions, which alter the magnetic reconnection process. Moreover, increasing the growth rate with the plasma parameters could be a source of anomalous resistivity that enhances the rate of magnetic reconnection.