Coherent laser beams in the 3 to 20 {mu}m region of the spectrum are most applicable for chemical sensing by addressing the strongest vibrational absorption resonances of the media. Broadband frequency combs in this spectral range are of special interest since they can be used as a powerful tool for molecular spectroscopy offering dramatic gains in speed, sensitivity, precision, and massive parallelism of data collection. Here we show that a frequency comb realized through subharmonic generation in an optical parametric oscillator (OPO) based on orientation-patterned gallium phosphide (OP-GaP) pumped by a Kerr-lens mode-locked 2.35-{mu}m laser can reach a continuous wavelength span of 3-12 {mu}m, thus covering most of the molecular signature region. The key to achieving such a broad spectrum is to use a low-dispersion cavity entailing all gold-coated mirrors, minimally dispersive and optically thin intracavity elements, and a specially designed pump injector. The system features a smooth ultra-broadband spectral output that is phase coherent to the pump laser comb, 245-mW output power with high (>20%) optical conversion efficiency, and a possibility to reach close to unity conversion from a mode-locked drive, thanks to the non-dissipative downconversion processes and photon recycling.