Here we demonstrate a self-directed project for undergraduate students that uses the design of a Hall effect thruster (HET) as a way to introduce fundamental physics concepts in lieu of traditional coursework. HET is a type of electric propulsion engine that uses orthogonal magnetic and electric fields to create a plasma that ionizes a propellant, which is then accelerated by a strong electric field to create thrust. The HET is used for many modern space applications, from station-keeping on small satellites to long-term travel to faraway asteroids.Electric propulsion, and specifically the HET, integrates many concepts that are fundamental in an undergraduate education such as electricity and magnetism (E&M), material properties, thermal analysis, and laboratory experimentation. However, the HET is rarely studied below the graduate level. As such, we present a path of feasibility for an undergraduate electric propulsion project building a small, low-power HET, both as a novel vehicle for engaging with introductory physics concepts and as a case study of an advanced self-directed project at the undergraduate level.In this paper we detail our process for developing a fundamental understanding of electric propulsion and demonstrate how to apply that learning to the design, manufacture, and test-fire of a small, low-power HET. Participants learned principles of E&M by modeling the magnetic field and channel, material properties and thermal analysis by designing the thruster components, and laboratory experiment by testing the thruster. We were able to complete this project with limited resources and within a single academic semester; to accommodate the constraints of integrating this project into undergraduate coursework, our HET was built with under $600 and using machinery found in a standard machine shop. Whereas typically a central concern in project based learning is ensuring a student begins a project with most of the skills needed to complete it, this paper outlines an extreme counterexample. We demonstrate that by taking advantage of student motivation, projects requiring skill sets far beyond those possessed by students at the beginning of the project can be both feasible and highly educational. Our hope is that readers of this paper will be able to use the design and construction of a low-power HET or similar projects in their own education as an applied way to learn fundamental physics while also customizing this project structure to address individual students' learning goals.