Artemis BJJ (MyGym/Bristol Sports Centre), Can Sönmez, Bristol, UK - 16/02/2015
On top of half guard, your opening goal is to get them flat on the mat: there are passes you can do while they are on their side, but generally speaking it is much easier if their back is pinned to the floor. A simple method, drawing on the Ribeiro brothers, is to drive your free knee into their hip, block their head with your same side arm, then step your trapped leg up and away from you. Having generated some space, drive the trapped knee forwards as your return it to the mat, which should also help you drive your opponent to the mat as well.
If you are able to get the cross-face and an underhook, there is now the option of generating lots of shoulder pressure. This is my favourite way to pass the half guard: both Saulo and his brother refer to this as the 'esgrima pass', but I call it the shoulder pressure pass in the interests of clarity. Cross-face their head (if you can't get the cross-face, you can also use your own head), so that they can't turn in that direction. Put your own head on the other side (or your arm, if you're already using your head to cross-face), locking their head into place: your shoulder and head work together to form a vice. It should now become hard for them to move their upper body, because their head is stuck.
From here, come up on your feet so that all your weight is driving through your shoulder. Even if you're small, this should maximise your weight. I'm only 66kgs, but if I can get all of that weight against somebody's head, it becomes more significant. From there, bounce your trapped knee to wriggle it free (if you're having trouble and need additional leverage, rotate your free leg back to hook their leg with your instep). As soon as it is clear of their legs, twist in the direction of your cross-facing arm and put that knee on the mat. You can then kick their leg off your foot: some people prefer to kick the top leg, but I would generally go for the bottom leg. Turning your hips to the ceiling can also help if you're struggling to get that foot loose.
Teaching & Sparring Notes: I think next time I'll make more of a point to go through that flattening out method I mention at the start. I wasn't sure if there was enough time to do that succinctly, but I think it's worth putting in. I'll also emphasise cutting across to other side with your knee. Although it's certainly possible to go straight to mount, IMO it's easier to cut across.
If they push your leg and move to recover guard, then it's probably best to switch to something else. That came up as Chris was doing it during progressive resistance. Asking him to do it to me, the natural counter felt like moving round to a firmer cross face as soon as he tries to grab the leg, or perhaps going for the arm. The next should be more vulnerable too if they're committing their arm like that, which reminds me to revise some chokes from top half guard.
I'm making a point of jumping in with specific sparring, now that my groin injury seems to be a lot better (I'm still wary of certain sweeps, but for the last couple of weeks I've been able to spar fairly normally). I was looking to pop under to deep half off Braulio's arm shield, but only managed it the once (during the later open mat sparring). Mainly I was grabbing the toes and going for that toe grab sweep. A number of times I went for the Bravo version, because my other arm was stuck. It's definitely a good simplified option to have in your toolbox, though the more complex version is safer if you can get it.
When free sparring during the open mat, I was looking for that kimura from Ryan Hall's DVD. He does a knee block to open the half guard, which seemed to work well, or at least kept me in place when they tried to sweep. I also went for the americana later on. I sometimes worry that it's a strength move (given that's long been the americana's reputation), but then I'm doing it on people bigger than me, so hopefully there is some technique there (although these are people less experienced than me, so that no doubt helps a lot too).