  We compute the spectrum of linearized gravitational excitations of black
holes with substantial angular momentum in the presence of higher-derivative
corrections to general relativity. We do so perturbatively to leading order in
the higher-derivative couplings and up to order fourteen in the black hole
angular momentum. This allows us to accurately predict quasinormal mode
frequencies of black holes with spins up to about $70\%$ of the extremal value.
For some higher-derivative corrections, we find that sizable rotation enhances
the frequency shifts by almost an order of magnitude relative to the static
case.
