I have no idea and haven't tried it, but I'd be interested in trying methode champenoise on a beer like that (which is, I'm guessing, what they do).
You bottle condition with champagne yeast and then wait for it to carb, then you turn the bottle upside down and wait a looooooong time (remuage takes weeks to months). once the yeast has settled into the neck of the bottle, you freeze the neck so that the yeast cap will harden and the CO2 stays in solution for the next step, disgorge. Quickly turn the bottle right-side up, pop the cork or cap, and the yeast plug flies out, voila, yeast-free beer. Dosage comes next, adding a tiny bit of sugar depending on style, so as to offset the dryness from the bottle conditioning.
That's about it. I'd guess, given all of the champagne-like characteristics this beer is supposed to produce, that that's the method they use.