  We study gravitational perturbations of slowly-rotating black holes in a
general effective-field-theory extension of general relativity that includes up
to eight-derivative terms. We show that two Schr\"odinger-like equations with
spin-dependent effective potentials govern the odd - and even-parity master
variables. These equations are coupled for parity-violating corrections, and
this coupling affects the quasinormal modes even at linear order in the
higher-derivative corrections, due to their isospectrality in general
relativity. We provide results for the shifts in the fundamental quasinormal
mode frequencies at linear order in the spin, which we expect to be valuable
for high-precision phenomenology through future gravitational wave
observations.
