The luminescent property of 2D perovskite materials promotes their applications in light emitting diodes, phosphor powders, and scintillators. Recently, an interesting extrinsic low‐energy broadband luminescence is hotly investigated. However, the understanding of such emissions is still at the early stage. In this study, based on a modified solvent evaporation method, centimeter‐size (BDA)PbI4 (BDA = NH3C4H8NH32+) single crystals are grown which, besides the band–band emission, show a large Stokes‐shifted broadband luminescence. We find such emission can be effectively excited by sub‐gap photons and conclude defects‐induced shallow traps are the corresponding luminescence centers. Density functional theory (DFT) calculations indicate that in‐plane iodine vacancies can introduce shallow electron traps in the band gap and give rise to the broadband emission.