  We derive the cross-section for exclusive vector meson production in high
energy deeply inelastic scattering off a deuteron target that disintegrates
into a proton and a neutron carrying large relative momentum in the final
state. This cross-section can be expressed in terms of a novel gluon Transition
Generalized Parton Distribution (T-GPD); the hard scale in the final state
makes the T-GPD sensitive to the short distance nucleon-nucleon interaction. We
perform a toy model computation of this process in a perturbative framework and
discuss the time scales that allow the separation of initial and final state
dynamics in the T-GPD. We outline the more general computation based on the
factorization suggested by the toy computation: in particular, we discuss the
relative role of "point-like" and "geometric" Fock configurations that control
the parton dynamics of short range nucleon-nucleon scattering. With the aid of
exclusive $J/\Psi$ production data at HERA, as well as elastic nucleon-nucleon
cross-sections, we estimate rates for exclusive deuteron photo-disintegration
at a future Electron-Ion Collider (EIC). Our results, obtained using
conservative estimates of EIC integrated luminosities, suggest that
center-of-mass energies $s_{NN}\sim 12$ GeV$^2$ of the neutron-proton subsystem
can be accessed. We argue that the high energies of the EIC can address
outstanding dynamical questions regarding the short-range quark-gluon structure
of nuclear forces by providing clean gluon probes of such "knockout" exclusive
reactions in light and heavy nuclei.
