We study the coarsening dynamics of a two-dimensional system via numerical simulations. The system under consideration is a biphasic system consisting of domains of a dispersed phase closely packed together in a continuous phase and separated by thin interfaces. Such a system is elastic and typically out of equilibrium. The equilibrium state is attained via the coarsening dynamics, wherein the dispersed phase slowly diffuses through the interfaces, causing the domains to change in size and eventually rearrange abruptly. The effect of rearrangements is propagated throughout the system via the intrinsic elastic interactions and may cause rearrangements elsewhere, resulting in intermittent bursts of activity and avalanche behaviour. Here we aim at quantitatively characterizing the corresponding avalanche statistics (i.e. size, duration, and inter-avalanche time). Despite the coarsening dynamics is triggered by an internal driving mechanism, we find quantitative indications that such avalanche statistics displays scaling-laws very similar to those observed in the response of disordered materials to external loads.