We study the first-passage-time (FPT) properties of an active Brownian particle under stochastic resetting to its initial configuration, comprising its position and orientation, to reach an absorbing wall in two dimensions. We employ a renewal framework for the stochastic resetting process and use a perturbative approach for small Péclet numbers, measuring the relative importance of self-propulsion with respect to diffusion. This allows us to derive analytical expressions for the survival probability, the FPT probability density, and the associated low-order moments. Depending on their initial orientation, the minimal mean FPT for active particles to reach the boundary can both decrease and increase relative to the passive counterpart. The associated optimal resetting rates depend non-trivially on the initial distance to the boundary due to the intricate interplay of resetting, rotational Brownian noise, and active motion.