It's the thing that looks like a hard drive with a black plastic cover that has a rather thick wiring harness attached. It's the thing just to the left (as you face the engine) of the black plastic fuse box.
Thanks! I should be able to see it right away when I take a look. In Hondas, the ECU tends to be inside the car on the passenger side beneath a side panel cover.
Hey folks, small update: I found these DIYs for the mini at the following site: DIY Guides - totalMINI Forums Enjoy!