We describe the mechanism of self-aggregation of alpha-tocopherol transfer protein into a spherical nanocage employing Monte Carlo simulations. The protein is modeled by a patchy coarse-grained representation, where the protein-protein interfaces, determined in the past by X-ray diffraction, are represented by simplified two-body interaction potentials. Our results show that the oligomerization kinetics proceeds in two steps, with the formation of metastable trimeric units and the subsequent assembly into the spherical aggregates. Data are in agreement with experimental observations regarding the prevalence of different aggregation states at specific ambient conditions. Finally, our results indicate a route for the experimental stabilization of the trimer, crucial for the understanding of the physiological role of such aggregates in vitamin E body trafficking.