  We consider the production of a pair of heavy quarks and illustrate the
derivation of the MiNNLO method to match next-to-next-to-leading order
calculations with parton showers (NNLO+PS) for this class of processes. As a
first application, we construct an event generator for the fully differential
simulation of hadronic top-quark pair production at NNLO+PS and discuss all
details of its implementation in a parton shower Monte Carlo framework. We
present new phenomenological results for the Large Hadron Collider obtained by
including the tree-level decays of the top quarks, while accounting for
spin-correlation effects. A comprehensive comparison to LHC measurements shows
an excellent description of experimental data across multiple hadronic and
leptonic particle-level observables. The computer code is available for
download within the POWHEG-BOX.
