A current trend in software engineering is the model-driven software engineering approach, which emphasizes the use of formal models in the design phase to streamline the development process. The Unified Modeling Language (UML) has emerged as a widely adopted open-standard modeling approach. This paper introduces a Y-Design Formal Modeling Framework tailored for the efficient design and development of RESTful web service-based e-learning systems. Rooted in the 2-Track Unified Process (2TUP), the Y-Design framework structures the design process into three stages, each strategically employing selected UML diagrams: a functional stage focusing on capturing and modeling user requirements, a technical stage addressing architectural needs and defining system components, and a design-integration stage that harmonizes both tracks into a unified system. The feasibility and effectiveness of the proposed framework are validated through the implementation of a typical e-learning system, demonstrating its potential to streamline design while ensuring robust and scalable solutions for modern distributed systems. The proposed framework emphasizes agility and coherence, making it particularly suited for e-learning projects requiring modularity and efficient reuse of common e-learning users' required services.