Novel educational technologies and methodologies that create enthusiasm among students and promote learner engagement are becoming instructional priorities across all disciplines of STEM (Science, Technology, Engineering, and Mathematics). For example, Game-Based Learning has established itself as a methodology that addresses students engagement at different levels (student-centered learning, constructivist approach, shared social experience, systems thinking and so on). In this paper we show a generalized Game Design Methodology (GDM), which consists of four phases and includes the basic principles of the Universal Design for Learning (UDL) framework. Each phase of the proposed Universal Game-Design for Learning (UGDL) method is designed to allow students and teaching staff to develop the game and assess its progress throughout the entire process.