We report an embarrassingly parallel method for the evaluation of thermodynaproperties over an energy landscape exhibiting broken ergodicity, nested basin-samp(NBS). We also introduce the No Galilean U-Turn Sampler (NoGUTS), a new sapling scheme based on the No U-Turn Sampler (NUTS) introduced by Hoffman Gelman (2014) that works with the Galilean Monte Carlo scheme introduced by Betcourt (2012) to aid the efficient generation of new live points. NoGUTS can be thouof as a form of reflective slice sampling with an automatic stopping criterion. We ply this approach to a benchmark atomic cluster of 31 Lennard-Jones atoms, whexhibits a low temperature solid-solid heat capacity peak. The calculated heatpacity is compared with results generated by parallel tempering (PT), basin-samplparallel tempering (BSPT), and standard nested sampling (NS) simulations. NBSproduces the full heat capacity curve predicted by PT and BSPT, whilst the NS calation with similar computational cost fails to resolve the low temperature solid-sophase transition.