This study investigates the emergence of hurricane-like vortices in idealized simulations of rotating moist convection. A Boussinesq atmosphere with simplified thermodynamics for phase transitions is forced by prescribing the temperature and humidity at the upper and lower boundaries. The governing equations are solved numerically using a variable-density incompressible Navier-Stokes solver with adaptive mesh refinement to explore the behavior of moist convection under a broad range of conditions. In the absence of rotation, convection aggregates into active patches separated by large unsaturated regions. Rotation modulates this statistical equilibrium state so that the self-aggregated convection organizes hurricane-like vortices. The warm and saturated air converges to the center of the vortices, and the latent heat released through the upwelling forms the warm core structure. These hurricane-like vortices share characteristics similar to tropical cyclones in the earth's atmosphere. The hurricane-like vortices occur under conditionally unstable conditions where the potential energy given at the boundaries is large enough, corresponding to a moderate rate of rotation. This regime shares many similar characteristics to the tropical atmosphere indicating that the formation of intense meso-scale vortices is a general characteristics of rotating moist convection. The model used here does no include any interactions with radiation, wind-evaporation feedback, or cloud microphysics, indicating that, while these processes may be relevant for tropical cyclogenesis in the Earth atmosphere, they are not its primary cause. Instead, our results confirm that the formation and maintenance of hurricane-like vortices involve a combination of atmospheric dynamics under the presence of rotation and of phase transitions.