This paper examines the continuous casting process, a thermodynamic phenomenon similar to the two-phase Stefan problem, where heat is transferred between liquid and solid phases, separated by two moving interfaces that divide the domain into three distinct regions. Building on previous research related to uncontrolled heat distribution, we develop boundary feedback control strategies to regulate the process. Two independently operated cooling systems, positioned on either side of the casting apparatus, implement time-varying cooling rates during water spray cooling to influence solidification. By employing the backstepping method, we design controllers that stabilize the system at two specified reference set points, ensuring precise regulation of interface positions and uniform solidification. We demonstrate that accurate prediction and adjustment of cooling rates are crucial for achieving the desired slab quality and controlling the solidification rate. The proposed approach aims to show how backstepping control can effectively address a system of nonlinear partial differential equations (PDEs) with two moving boundaries. This method provides a systematic framework for enhancing stability and product quality in the continuous casting process.