In recent years, there has been extensive research on millimeter-wave (mmWave) communication and on in-band full-duplex (FD) communication, but work on the combination of the two is relatively lacking. FD mmWave systems could offer increased spectral efficiency and decreased latency while also suggesting the redesign of existing mmWave applications. While FD technology has been well-explored for sub-6 GHz systems, the developed methods do not translate well to mmWave. This turns us to a method called beamforming cancellation (BFC), where the highly directional mmWave beams are steered to mitigate self-interference (SI) and enable simultaneous transmission and reception in-band. In this paper, we present BFC designs for two fully-connected hybrid beamforming scenarios, both of which sufficiently suppress the SI such that the sum spectral efficiency approaches that of a SI-free FD system. A simulation and its results are then used to verify our designs.