  Gravitational-wave (GW) observations of neutron star-black hole (NSBH)
mergers are sensitive to the nuclear equation of state (EOS). We present a new
methodology for EOS inference with non-parametric Gaussian process (GP) priors,
enabling direct constraints on the pressure at specific densities and the
length-scale of correlations on the EOS. Using realistic simulations of NSBH
mergers, incorporating both GW and electromagnetic (EM) selection to ensure
sample purity, we find that a GW detector network operating at O5-sensitivities
will constrain the radius of a $\unit[1.4]{M_{\odot}}$ NS and the maximum NS
mass with $1.6\%$ and $13\%$ precision, respectively. With the same sample, the
projected constraint on the length-scale of correlations in the EOS is
$\geq~\unit[3.2]{MeV~fm^{-3}}$. These results demonstrate strong potential for
insights into the nuclear EOS from NSBH systems, provided they are robustly
identified.
