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QGP, a strongly coupled liquid when viewed at length scales of ${\cal O}(1/T)$, must reveal quark- and gluon-like quasi-particles when probed with sufficiently high momentum transfer, since QCD is asymptotically free. High energy jet partons traversing the droplet of QGP produced in a heavy ion collision can trigger these high-momentum exchanges with medium constituents and so have the potential to reveal the presence of such quasi-particles, a key step toward the experimental study of the microscopic structure of QGP. We implement this physics within the hybrid strong/weak coupling model which, prior to this work, only accounted for nonperturbative aspects of parton energy loss. Elastic Molière scatterings between partons from a jet shower and medium quasi-particles result in deflection of the propagating jet partons and struck thermal medium partons recoiling at large angles. We discuss the effect of Molière scatterings on some of the most widely used groomed and ungroomed jet substructure observables. Given the large impact on jet observables of the wakes generated by the hydrodynamic response of the QGP fluid as the shower and scattered partons lose energy and momentum to it, as well as the presence of selection biases, finding distinctive signatures of Molière scattering, and hence the presence of quasi-particles in QGP, is a challenge. Toward this end, we emphasize the discovery potential of subjet (jets within jets) distributions.