Ah ha! Figured it out.
Create a block at the top of the base layout and add your variables in there.
_layout.jade:
block variables
doctype html
html(lang="en-au")
head
meta(charset="utf-8")
block css
body(class=(body_class || "it-did-not-work"))
block header
block content
block footer
home.jade:
extends _layout
block variables
- var body_class="i-am-the-home-page"
block header
h1 home