Q: What is an Exceptional Exception?
A: It's a rare and exotic species of exception. One that defies categorization, but is still somehow categorizable.
Q: How do I become an Exceptional Exception?
A: You don't. It's not something you can become, per se. But you can certainly try to be an exception to the exceptions.
See also: Exceptional Exceptions FAQ 2, Exceptional Exceptions FAQ 2, Exceptional Exceptions FAQ 3