An optical antenna can convert a propagative optical radiation into a localized excitation, and reciprocally. Although optical antennas can be readily created using resonant nanoparticles (metallic or dielectric) as elementary building blocks, the realization of antennas sustaining multiple resonances over a broad range of frequencies remains a challenging task. Here, we use aluminum self-similar, fractal-like structures as broadband optical antennas. Using electron energy loss spectroscopy, we experimentally evidence that a single aluminum Cayley tree, a simple self-similar structure, sustains multiple plasmonic resonances. The spectral position of these resonances is scalable over a broad spectral range spanning two decades, from ultraviolet to mid-infrared. Such multi-resonant structures are highly desirable for applications ranging from non-linear optics to light harvesting and photodetection, as well as surface-enhanced infrared absorption spectroscopy.