Beyond the Standard Model physics is required to explain both dark matter and the baryon asymmetry of the universe, the latter possibly generated during a strong first-order electroweak phase transition. While many proposed models tackle these problems independently, it is interesting to inquire whether the same model can explain both. In this context, we link state-of-the-art perturbative assessments of the phase transition thermodynamics with the extraction of the dark matter energy density. These techniques are applied to a next-to-minimal dark matter model containing an inert Majorana fermion that is coupled to Standard Model leptons via a scalar mediator, where the mediator interacts directly with the Higgs boson. For dark matter masses 180 GeV < M_χ ≲ 300 GeV, we discern regions of the model parameter space that reproduce the observed dark matter energy density and allow for a first-order phase transition, while evading the most stringent collider constraints.