Note- Bill rolled up with a broken half of his regular paddle, not with a spare off of his deck. In many ways, this is more challenging, as while you are underwater you need to feel around and figure out what is going on and how to make it work. Looks like it is opposite blade from what he would have used for that roll with a full paddle, so he had to swing the blade around from one side of his boat to the other to make it work. Rolling with a spare off deck would have been something he has practiced before, so he’d know exactly where the half paddle is and how it is laid out, so it would have been grab and go.
Not the first time this has been done, nor caught on film. Here is Sergey from a few years ago when he broke his wooden GP on a large pourover, and had to figure out how to make it work to roll up.
Note - if you back the video up to start at time 3:29, you will see Sergey’s wife going over a bigger, super impressive wave and need to roll up, but she doesn’t have paddle issues, so that run isn’t relevant to this conversation.
Edit - looks like Youtube doesn’t bring over the second part of time stamps, only minutes. The Sergey roll is at 3:51.