Energy-correlator-based jet substructure has gained significant attention in recent years. One of the notable applications has been the study of multi-scale jets, where distinct physical scales manifest as features localised in different angular regions of the correlator. In this article, we present the first high-precision study of energy correlators on the simplest multi-scale jets: heavy boson jets. In such systems, the boson mass M introduces an additional scale, generating a sharp peak at angles ~ \( M/{p}_T^{\mathrm{jet}} \) . We show that this feature can be computed directly by boosting the EEC spectrum measured in e+e− → hadrons at the Z pole. We identify that the peak arises from boosting the well-studied Sudakov factorisation governing the back-to-back limit of the two-point correlator. As a result, the feature is controlled by Sudakov resummation, not a Breit-Wigner-like structure in the Z decay, and is therefore calculable with exceptional precision. We provide predictions at N3LL′ accuracy for both pp Z-tagged jets and e+e− di-Z production, and compare them to Herwig and Pythia simulations, finding close agreement. We also demonstrate that the boosted-Z spectrum can be constructed directly by boosting OPAL measurements at the Z pole. In this light, energy-correlator jet substructure on the hadronic decays of heavy bosons at the LHC provide access to clean, lepton-collider-like measurements across a wide range of effective centre-of-mass energies set by the boson jet transverse momentum.