  The Effective Field Theory (EFT) of perturbations on an arbitrary background
geometry with a timelike scalar profile was recently constructed in the context
of scalar-tensor theories. In this paper, we use this EFT to study quasinormal
frequencies of odd-parity perturbations on a static and spherically symmetric
black hole background. Keeping a set of operators that can accommodate
shift-symmetric quadratic higher-order scalar-tensor theories, we demonstrate
the computation for two examples of hairy black holes, of which one is the
stealth Schwarzschild solution and the other is the Hayward metric accompanied
by a non-trivial scalar field. We emphasize that this is the first
phenomenological application of the EFT, opening a new possibility to test
general relativity and modified gravity theories in the strong gravity regime.
