The past few years have witnessed impressive developments in optical sources capable of emitting structured forms of light, such as optical vortices or vector beams. Because structured beams result from carefully engineered interferences, their synthesis requires coherent light and all the sources demonstrated so far rely on coherent lasing cavities-usually pumped with external optical schemes. Here, we introduce non-lasing sources emitting directional vortex beams upon electrical injection. Their architecture consists of colloidal PbS quantum dot LEDs that integrate a photonic environment with two complementary functions: to make the emitters populate radial photonic modes with extended spatial coherence, and to structure the leakage of these modes into free space. Our electrically-pumped sources exhibit phase singularities across the electroluminescence spectrum of the quantum dots, leading to vortex light emission with a bandwidth of 300 nm in the near-infrared.