An optical antenna can convert a propagative optical radiation into a localized excitation and the reciprocal. 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 midinfrared. Such multiresonant structures are highly desirable for applications ranging from nonlinear optics to light harvesting and photodetection, as well as surface-enhanced infrared absorption spectroscopy.