I've read some conflicting information about this. Some say do it on an empty stomach first thing in the morning, others after eating something such as a protein shake.

What's the general consensus?

leave the horse alone it is dead. With a quick study of a few threads you can see arguments for both, and it all comes down to doing what works for you.

if your doing HIIT i would strongly suggest eating, lower-intensity cardio is another issue, you will have to do some research and decide for yourself