Artemis BJJ (MYGYM Bristol), Can Sönmez, Bristol, UK - 20/04/2015
Starting from high mount, keep low, your arm based out, putting your head on the same side to concentrate your weight. Remember to keep your feet tucked under their bum for control. Drive your first grip in, which normally is going to be blocked by their arms crossed over their chest. To work past that, Roger advises that you pull open their collar low on their lapel (or at least lower than their elbows. You don't want to get stuck trying to yank out the collar from directly underneath their tightly crossed arms). You can then slide your arm through. To make that extra-solid, Roger Gracie told me to brace your own elbow against your hip. You can then wriggle forwards, driving your arm in front of you with the combined power of your hips, legs and arm. Also form your hand into a wedge, as this will help cut past their blocking arms.
Either way, once you have the grip, lift them up towards you slightly, twisting your hand so that you create a small gap between their neck and collar. Into that gap, insert the thumb of your free hand, to establish your second grip. You can also drop your elbow to the other side, so that you're pressuring into their neck.
Slide that thumb behind their head to the other side of their neck. As you do, also move your head to the other side of their head. Next, bring the arm of your thumb grip to the other side of their head, 'shaving' close to their face. This is to set up the choke, putting your wrists on both sides of their neck.
Once you've got the thumb arm into position, so that both carotid arteries are blocked off, move your forehead to the floor directly above their head. Twist your wrists and drop your weight into them to finish the choke. Roy Dean provides a handy pointer here, which is to shift your hips forward slightly, still basing on your head. That will give you a little extra leverage, should you need it.
I focused on my preferred cross choke variation from Michel Verhoeven. After you've inserted your first hand, start to raise your partner towards you slightly. Bring your second arm around to the other side of their head, then 'shave' back across their face to position that arm by their neck. Grab a handful of gi by their shoulder, then drop your elbow so your forearm is over their throat. This second arm doesn't move after that point: the choke comes from twisting the first hand and drawing that first elbow back.
Teaching Notes: Pushing past that defending hand was a slight problem for a few people, though it seemed that eventually everyone could get through. However, I'm not sure if that is merely a matter of force, or something more refined. Hopefully it comes down to leverage rather than brute strength: I was advising people to bring their whole body to bear, rather than just shoving with their hand. Instead, having braced their elbow against their hip (like Roger says), they should also be driving with their hips, feet, legs and using their body weight to get that hand into position.