When driving to Exomania, Lars and Joe stopped at a Mediterranean restaurant in the middle of nowhere. A cashier named Brittany took their orders, and Joe instantly found himself attracted to her. As they walked out, Lars dared Joe repeatedly to get her number. A few minutes later, he walked out with success.
Nothing ultimately came of this in terms of Joe's dating life, but "Brittany" as a concept has mutated into sort of a metaphysical placeholder for Joe's "Euclidian ideal" of a woman.
Both hosts have expressed amusement toward the technically possible future event that the real Brittany will someday listen to the podcast by chance, notice that the weird customer from work talks about her a lot on air, and be deeply concerned.