My goal is to use the BRIX as the platform which houses 3 ESXi hosts (which will be created as virtual machines).
Let me just save you some time here since I've worked with these systems. What you're wanting to do, although it makes perfect sense, is really, really not going to work well. That BRIX system is a miniaturized PC, like the Intel NUC platform. As a result of that compact form factor, the CPUs used within have to drastic reign it in to the tune of only about 15W TDP. Even though you get 4 cores, they're very tuned down. Now you're sharing that with a parent ESXi host plus others in nested mode (each of which requires 2 cores to install). The results are going to just plain suck, I'm sorry to say.
It's much more common and far more performant to have 3 BRIX/NUCs and run a lab on that (i.e., non-nested) and, while this obviously costs more, it'll at least run half-way decent.
In short, what you want--even if you achieve it--is going to run terrible and will result in a lab which isn't capable of much at all and in which performance across the board will be abysmal. Save yourself some hassle and either upsize to a full workstation tower, or plan to buy multiple miniature systems to cluster for a complete lab setup.
