Broken scarf hold is a variation of kesa gatame where the top player takes his arm off your head and slides it under your far arm instead. In Japanese it's kuzure kesa gatame. Same scarf hold posture, different arm path — and it's even harder to get out of.
Scott's not big on the Japanese names. What matters is what it does to you.
Here's why broken scarf is nastier. In regular kesa, when you bridge into him and his weight shifts, he has to post a hand — and when he posts, his head comes off you. In broken scarf, he can post, keep his balance, AND still stay tight under your arm. No buffer for you. Big dudes can flatten you out with this one and it really sucks.
The good news? He has fewer attacks from here. The other good news is that he can't bury his head as well. In regular kesa, guys hide their chin down tight and you have to weasel your frame in with fingertips. In broken scarf, his head is further away. There's no arm wrapped around your face. You can get a hand in easier.
And that's the whole key to Scott's favorite escape from here.
Set it up like you're about to bonk him with your hips one way. Sell it hard — hips in the air, all your energy committed in that direction. His base reacts. Then snap back the other way and karate chop his face backwards with your free hand. Push the head as far down as you can. The further it goes, the easier the leg comes over. One, two, leg over the head, and you're out.
It has to be a surprise move. No surprise, no escape.
For the bigger picture on this position, read our full guide to escaping side control. The complete course lives inside Scott Sullivan's BJJ 101 System.