Some neutron star X-ray transients (the quasi-persistent transients) spend an unusually long time in outburst, with outbursts lasting years to decades rather than the usual weeks to months. During these outbursts, the neutron star crust gets heated significantly out of thermal equilibrium with the core and thus once back in quiescence, the crust thermally radiates X-rays, cooling it down until reaching thermal equilibrium again. Crust cooling curves allow us to probe the properties of neutron stars. We present Chandra and XMM-Newton X-ray observations that track the neutron star cooling of the 2 quasi-persistent neutron star X-ray transients MXB 1659-29 and KS 1731-260. The results of our analysis strengthen the preliminary findings of Wijnands et al. that in both sources the neutron star crust cools down very rapidly, suggesting it has a high heat conductivity and that the neutron star core requires enhanced core cooling processes. Importantly, we now detect the flattening of the cooling in both sources as the crust returns to thermal equilibrium with the core. This is the first time that the cooling of a neutron star crust into thermal equilibrium with the core has been observed in such detail.