  We develop a theory of electron tunneling accompanied by carrier-carrier
scattering in graphene - insulator - graphene heterostructures. Due to the
dynamic screening of Coulomb interaction, the scattering-aided tunneling is
resonantly enhanced if the transferred energy and momentum correspond to those
of surface plasmons. We reveal the possible experimental manifestations of such
plasmon-assisted tunneling in current-voltage curves and plasmon emission
spectra of graphene-based tunnel junctions. We find that inelastic current and
plasmon emission rates have sharp peaks at voltages providing equal energies,
momenta and group velocities of plasmons and interlayer single-particle
excitations. The strength of this resonance, which we call plasmaronic
resonance, is limited by interlayer twist and plasmon lifetime. The onset of
plasmon-assisted tunneling can be also marked by a cusp in the junction
$I(V)$-curve at low temperatures, and the threshold voltage for such tunneling
weakly depends on carrier density and persists in the presence of interlayer
twist.
