Modern computer systems are exceedingly complex, and increasingly so. This makes it challenging for students with no background in computer systems to climb the mountain of 40 years of design, particularly within a constrained teaching timetable. Through the medium of FPGAs, we have designed an 8-week course to take students from basic digital electronics through to processor design, modern software tools, applications, system-on-chip integration and electronics manufacturing. We recount our experiences with rapidly bringing students up to speed with the modern world of computing systems, and some of the lessons we, as course designers, were taught by the process.