In this note, a novel technique, referred to as the di- tagger, is designed to reconstruct and identify hadronically decaying pairs with a large Lorentz boost in the ATLAS experiment at the Large Hadron Collider. A benchmark di- tagging selection is employed in the search for resonant Higgs boson pair production, where one Higgs boson decays into a boosted pair and the other into a boosted pair, with two hadronically decaying -leptons in the final state. The efficiency of the di- tagger is measured for this benchmark using 139 fb of proton-proton collision data recorded at a centre-of-mass energy of 13 TeV, and the background with quark- or gluon-initiated jets misidentified as di- objects is estimated. The search for a heavy, narrow-width, scalar resonance produced via gluon-gluon fusion and decaying into two Higgs bosons is carried out in the mass range 1-3 TeV using the same dataset. No deviations from the Standard Model predictions are observed and 95% confidence-level exclusion limits are set on this model.