We report the electromagnetically-induced-transparency (EIT) cooling of a large trapped Yb-171(+) ion chain to the quantum ground state. Unlike conventional EIT cooling, we engage a four-level tripod structure and achieve fast sub-Doppler cooling over all motional modes. We observe simultaneous groundstate cooling across the complete transverse mode spectrum of up to 40 ions, occupying a bandwidth of over 3 MHz. The cooling time is observed to be less than 300 mu s, independent of the number of ions. Such efficient cooling across the entire spectrum is essential for high-fidelity quantum operations using trapped ion crystals for quantum simulators or quantum computers.