Understanding the mechanisms in charge of ``shaping'' hadrons inside is among the most charming problems in physics. Indeed, new experimental facilities such as the EIC are planned, and an unprecedented amount of information about hadron's complexity is expected to arise. This work takes advantage of the current situation to perform the first systematic feasibility study of accessing pion's structure at an electron-ion collider. We employ state-of-the art models for generalized parton distributions to compute the amplitude for Deeply Virtual Compton Scattering (DVCS) in the one-pion exchange approximation at EIC kinematic. Predictions for the expected event-rates and beam-spin asymmetries are shown. We demonstrate that DVCS off virtual pions will be measurable at the EIC. Moreover, we evince that gluons play the dominant role, modulating the expected number of events through interference with the quark distribution. Finally, a sign-inversion for the observed beam-spin asymmetries is found to take place, triggering a clear signal for a glue-led regime.