We consider a singlet extension of the standard model (SM) with a spontaneous Z2 breaking and study the gluon-gluon fusion production of the heavy scalar, with subsequent decay into a pair of SM-like Higgs bosons. We find that an on-shell interference effect can notably enhance the resonant di-Higgs production rate up to 40%. In addition, consistently taking into account both the on-shell and off-shell interference effects between the heavy scalar and the SM di-Higgs diagrams significantly improves the HL-LHC and HE-LHC reach in this channel. As an example, within an effective field theory analysis in an explicitly Z2 breaking scenario, we further discuss the potential to probe the parameter region compatible with a first-order electroweak phase transition. Our analysis is applicable for general potentials of the singlet extension of the SM as well as for more general resonance searches.