We present the νϕMTH, a Mirror Twin Higgs (MTH) model realizing asymmetric reheating, baryogenesis and twin-baryogenesis through the out-of-equilibrium decay of a right-handed neutrino without any hard $${\mathbb{Z}}_{2}$$ breaking. The MTH is the simplest Neutral Naturalness solution to the little hierarchy problem and predicts the existence of a twin dark sector related to the Standard Model (SM) by a $${\mathbb{Z}}_{2}$$ symmetry that is only softly broken by a higher twin Higgs vacuum expectation value. The asymmetric reheating cools the twin sector compared to the visible one, thus evading cosmological bounds on ∆Neff. The addition of (twin-)colored scalars allows for the generation of the visible baryon asymmetry and, by the virtue of the $${\mathbb{Z}}_{2}$$ symmetry, also results in the generation of a twin baryon asymmetry. We identify a unique scenario with top-philic couplings for the new scalars that can satisfy all cosmological, proton decay and LHC constraints; yield the observed SM baryon asymmetry; and generate a wide range of possible twin baryon DM fractions, from negligible to unity. The viable regime of the theory contains several hints as to the possible structure of the Twin Higgs UV completion. Our results motivate the search for the rich cosmological and astrophysical signatures of twin baryons, and atomic dark matter more generally, at cosmological, galactic and stellar scales.