Ok, I swear I know how to do this! However, it appears to have slipped my mind, and it's starting to frustrate me that I can't remember... ;)
If I install CentOS 6 without the Anaconda installer it will install a "minimal" install by default. However, the minimal install is missing basic utilities such as wget, and I would like to install the "basic server" profile onto it after-the-fact.
So, to summarize: How do I Install the "Basic Server" Profile onto a "Minimal" Install of CentOS?