Truth be told, my brainstorming technique could do with an upgrade.
Basically, the way it works for me is that once I have the nutshell for the script, I start generating as many ideas for it as possible. These may be big story beats or smaller moments, single gags... There's always a first rush of ideas which comes along with the initial conception of the story. Afterwards, I'm usually a little blocked, and have to put more effort into coming up with more. Usually, physical action helps me in breaking through barriers and solving story problems. Too bad I'm not a very physical person, then...
I find I need to write my brainstorms down on paper. Sitting at the PC doesn't seem to work for me at this point in the creative process - at least not very well. Luckily it doesn't hamper my creativity when I'm actually writing the synopsis or dialogue drafts.
Usually I also start structuring the story in this phase. When I'm really blocked, it's often because I forget to ask the age-old question: whose story is it anyway? In my defense, when you're writing a script for FC De Kampioenen, which has 10+ main characters (i.e. every cast member can be the lead in a story, there's no primary/secondary/tertiary character hierarchy), this question can be pretty hard to answer at times. If only because every character needs to be accounted for and given something to do in the script (we don't let characters stay off-screen except on rare occassions where an actor is unavailable because of health reasons).
Once I have the feeling that I've gathered enough material for the script in question, and I have a workable structure set up, it's then time to move on to the next step: the beat sheet or step outline.