Gluon TMDs can be probed in an almost back-to-back production
of J/psi and a photon/jet/pion in ep collision. We present a summary of
our recent calculations of azimuthal asymmetries in such processes using a
TMD factorized framework, in the kinematics to be accessed by the upcoming
EIC. We use NRQCD to estimate the J/psi production, and use recent
parametrizations of the gluon TMDs. Our results show that the asymmetries
are sizable and will be useful to probe in particular the gluon Sivers
function and linearly polarized gluon distributions.