Computer architecture lies at the intersection of electrical engineering, digital design, compiler design, programming language theory and high-performance computing. It is considered a foundational segment of an electrical and computer engineering education. RISC-V is a new and open ISA that is gaining significant traction in academia. Despite it being used extensively in research, more RISC-V-based tools need to be developed in order for RISC-V to gain greater adoption in computer organization and computer architecture classes. To that end, we present the BRISC-V Platform, a design space exploration tool which offers: (1) a web-based RISC-V simulator, which compiles C and executes assembly within the browser, and (2) a web-based generator of fully-synthesizable, highly-modular and parametrizable hardware systems with support for different types of cores, caches, and network-on-chip topologies. We illustrate how we use these tools in teaching computer organization and computer architecture classes, and describe the structure of these classes.