We theoretically and experimentally investigate double-electromagnetically-induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for ^{171}Yb^{+} ions with a clock state, for which EIT cooling has not been realized like many other ions with a simple Λ scheme. A cooling rate of n[over ¯][over ˙]=34(±1.8) ms^{-1} and a cooling limit of n[over ¯]=0.06(±0.059) are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12-ion crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences.