Investigating students' thinking in classroom tasks, particularly in science and engineering, is essential for improving educational practices and advancing student learning. In this context, the notion of "Ways of Thinking" (WoT) has gained traction in STEM education, offering a framework to explore how students approach and solve interdisciplinary problems. Building on our earlier studies and contributing to ongoing discussions on WoT frameworks, this paper introduces a new WoT framework--Ways of Thinking in Engineering Design-based Physics (WoT4EDP). WoT4EDP integrates five key elements--design, science, mathematics, metacognitive reflection, and computational thinking--within an undergraduate introductory physics laboratory. This novel framework highlights how these interconnected elements foster deeper learning and holistic problem solving in ED-based projects. A key takeaway is that this framework serves as a practical tool for educators and researchers to design, implement, and analyze interdisciplinary STEM activities in physics classrooms. We describe the development of WoT4EDP, situate it within undergraduate STEM education, and characterize its components in detail. Additionally, we compare WoT4EDP with two contemporary frameworks--Dalal et al. (2021) and English (2023)--to glean insights that enhance its application and promote interdisciplinary thinking. This paper is the first of a two-part series. In the upcoming second part, we will demonstrate the application of the WoT4EDP framework, showcasing how it can be used to analyze student thinking in real-world, ED-based physics projects.