The self-organization of confined, quasi-two-dimensional turbulent flows in a rotating square container with a step-like topography is investigated by means of laboratory experiments and numerical simulations based on a rigid lid, shallow-water formulation. The domain is divided by a bottom discontinuity into two rectangular regions, one being shallow and the other deep. The existence of a preferential vorticity distribution in the long-term evolution of the decaying flow is discussed. Initially, the turbulent flow organizes into larger structures. After a few rotation periods, a continuous jet-like flow is consistently observed along the step, with the shallow region at its right. This flow is associated with the adjustment of the fluid to equilibrium over a bottom discontinuity in an anti-clockwise rotating system. At the end of the step, two persistent structures are formed due to the collision of this jet with the vertical wall: a cyclonic circulation cell in the deep region, while an anticyclonic cell occurs in the shallow part of the domain. The laboratory experiments are well-reproduced by the simulations. Due to bottom friction effects, the fluid motion is halted before a complete organization of the flow is accomplished. In order to study the full process, additional numerical simulations were performed with zero Ekman friction. Same principal features are observed as in the experiments, but now a complete organization of the flow into four vortices is obtained: in the deep part of the flow domain, a cyclone-anticyclone pair is observed that fills up the entire region, and the mirrored double cell structure occurs on the shallow side. Such a disposition of the vortices is directly associated with the interaction of the flow along the step and the downstream wall at which it collides, as observed in the experiments. It is shown that this arrangement is systematically obtained in simulations with very different initial conditions. The existence of a preferential vorticity distribution induced by a topographic step is further discussed in terms of the aspect ratio of the domain.