Popularity of metasurfaces has been continuouslygrowing due to their attractive properties including the ability to effectively manipulate electromagnetic (EM) waves. Metasurfaces comprise optimized geometries of unit cells arranged as a periodic lattice to obtain a desired EM response. One of their emerging application areas is the stealth technology, in particular, realization of radar cross section (RCS) reduction. Despite potential benefits, a practical obstacle hindering widespread metasurface utilization is the lack of systematic design procedures. Conventional approaches are largely intuitioninspired and demand heavy designer's interaction while exploring the parameter space and pursuing optimum unit cell geometries. Not surprisingly, these are unable to identify truly optimum solutions. In this article, we introduce a novel machine-learningbased framework for automated and computationally efficient design of metasurfaces realizing broadband RCS reduction. Our methodology is a three-stage procedure that involves global surrogate-assisted optimization of the unit cells, followed by their local refinement. The last stage is direct EM-driven maximization of the RCS reduction bandwidth, facilitated by appropriate formulation of the objective function involving regularization terms. The appealing feature of the proposed framework is that it optimizes the RCS reduction bandwidth directly at the level of the entire metasurface as opposed to merely optimizing unit cell geometries. Computational feasibility of the optimization process, especially its last stage, is ensured by high-quality initial designs rendered during the first two stages. To corroborate the utility of our procedure, it has been applied to several metasurface designs reported in the literature, leading to the RCS reduction bandwidth improvement by 15%-25% when compared with the original designs. Furthermore, it was used to design a novel metasurface featuring over 100% of relative bandwidth. Although the procedure has been used in the context of RCS design, it can be generalized to handle metasurface development for other application areas.