  We consider a singlet extension of the Standard Model (SM) with a spontaneous
$Z_2$ 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 $Z_2$ 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.
