We studied the spontaneous emulsification and droplet growth mechanism in trans-anethol/water/ethanol solutions, also known as the beverage ouzo, using dynamic light scattering spectroscopy. This simple ternary mixture is a generic example of a system that forms microemulsions spontaneously when brought into the two-phase region. The volume fraction of the dispersed phase was found to profoundly affect the growth rates of the droplets, which is a new finding that has not been predicted by the Lifshitz-Slyozov-Wagner theory. Time-dependent measurements show that the droplet growth is governed by Ostwald ripening (OR), and no coalescence was observed. Furthermore, the OR rates increase with increasing oil concentration at low alcohol content. We attribute this behavior to enhanced droplet-droplet interactions. At high ethanol concentrations, we found that the measured rates decreased as the oil concentration increased. The OR growth mechanism completely correlates with changes in droplet size. The kinetics of droplet growth shows that the ripening has a saturation limit at a droplet radius of about 1.5 mum. Thus, formed emulsions remain stable for months.