Controlling the directionality of emitted far-field thermal radiation is a fundamental challenge. Photonic strategies enable angular selectivity of thermal emission over narrow bandwidths, but thermal radiation is a broadband phenomenon. The ability to constrain emitted thermal radiation to fixed narrow angular ranges over broad bandwidths is an important, but lacking, capability. We introduce gradient epsilon-near-zero (ENZ) materials that enable broad-spectrum directional control of thermal emission. We demonstrate two emitters consisting of multiple oxides that exhibit high (>0.7, >0.6) directional emissivity (60° to 75°, 70° to 85°) in the p-polarization for a range of wavelengths (10.0 to 14.3 micrometers, 7.7 to 11.5 micrometers). This broadband directional emission enables meaningful radiative heat transfer primarily in the high emissivity directions. Decoupling the conventional limitations on angular and spectral response improves performance for applications such as thermal camouflaging, solar heating, radiative cooling, and waste heat recovery.