Motivated by the industrial processing of chocolate, we study experimentally the fluidisation of a sessile drop of yield-stress fluid on a pre-existing layer of the same fluid under vertical sinusoidal oscillations. We compare the behaviours of molten chocolate and Carbopol which are both shear-thinning with a similar yield stress but exhibit very different elastic properties. We find that these materials spread when the forcing acceleration exceeds a threshold which is determined by the initial deposition process. However, they exhibit very different spreading behaviours: whereas chocolate exhibits slow long-term spreading, the Carbopol drop rapidly relaxes its stress by spreading to a new equilibrium shape with an enlarged footprint. This spreading is insensitive to the history of the forcing. In addition, the Carbopol drop performs large-amplitude oscillations with the forcing frequency, both above and below the threshold. We investigate these viscoelastic oscillations and provide evidence of complex nonlinear viscoelastic behaviour in the vicinity of the spreading threshold. In fact, for forcing accelerations greater than the spreading threshold, our drop automatically adjusts its shape to remain at the yield stress. We discuss how our vibrated-drop experiment offers a new and powerful approach to probing the yield transition in elastoviscoplastic fluids.