  We report the electromagnetically-induced-transparency (EIT) cooling of a
large trapped $^{171}$Yb$^+$ 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
ground-state 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.
