We present radio continuum mapping, optical imaging, and spectroscopy of the newly discovered double-peaked, broad-lined active galactic nucleus (AGN) WISE J233237.05−505643.5 at redshift z = 0.3447. This source exhibits an FR-I and FR-II hybrid morphology, characterized by a bright core, jet, and Doppler-boosted lobe structures in Australian Telescope Compact Array continuum maps at 1.5, 5.6, and 9 GHz. Unlike most FR-II objects, W2332−5056 is hosted by a disk-like galaxy. The core has a projected 5 linear radio feature that is perpendicular to the curved primary jet, hinting at unusual and complex activity within the inner 25 kpc. The multiepoch, optical-near-IR photometric measurements indicate significant variability over a 3-20 yr baseline from the AGN component. Gemini South optical data show unusual double-peaked emission-line features: the centroids of the broad-lined components of Hα and Hβ are blueshifted with respect to the narrow lines and host galaxy by ∼3800 km s −1 . We examine possible cases that involve single or double supermassive black holes in the system and discuss the required future investigations to disentangle the mysterious nature of this system.