Many asymmetric dark matter scenarios have been proposed to date. Among them, perhaps the most motivated ones are those in which the dark matter asymmetry is induced from the baryon/lepton asymmetries via chemical equilibration without any new sources of CP violation. However, most of the models put forward along these lines have been excluded by now and/or are based on complicated setups. In this letter, we present a new, simple, and viable scenario. It assumes only two new fields: a scalar singlet and an inert scalar doublet, and is based only on renormalizable interactions, that slowly generate the dark matter asymmetry from the Standard Model Higgs asymmetry. The successful asymmetry transfer requires small (but technically natural) couplings which in turn make the model CP conserving in practice. The model allows for the direct detection of dark matter in the upcoming generation of experiments, and the inert doublet is predicted to be light enough to be potentially produced and observed at the LHC and future colliders, 46 GeV < mH’ < 580 GeV. Quite remarkably, the mass and lifetime of the inert doublet may be inferred from direct detection experiments, indicating long-lived compressed electroweak states that can be searched for at the HL-LHC.