  We detail a simulation of Higgs boson production via gluon fusion, accurate
at next-to-next-to-leading order in the strong coupling, including matching to
a parton shower, yielding a fully exclusive, hadron-level description of the
final-state. The approach relies on the POWHEG method for merging the NLO Higgs
plus jet cross-section with the parton shower, and on the MINLO method to
simultaneously achieve NLO accuracy for inclusive Higgs boson production. The
NNLO accuracy is reached by a reweighting procedure making use of the HNNLO
program.
