I can tell you exactly what it is. Had the SAME exact issue with an 05.5 jetta TDi my mom purchased recently.
It's the wastegate actuator located right behind the cylinder head almost dead center. The actuator sticks, and causes the ASV to stick and block exhaust flow from spooling the turbine. You get the sensation of NO acceleration and a plume of black smoke from the exhaust, then all the sudden it pops and the car takes off. Do this...
Take the vacuum line off of that wastegate actuator. Get a can of lubricant (WD40 for example). Spray it into the actuator. Hook up some sort of vacuum device and put the actuator under vacuum. Watch the actuator rod move back and forth till it starts moving free and smooth. Put the vacuum line back on and take it for a good ride. It's been maybe 1k miles since I've done this and she hasn't been able to duplicate the problem. She knew exactly when it would do it in whatever situation, and it refuses to happen again.
VW's remedy is to replace the turbo, as this actuator is part of the wastegate which is part of the turbo, which no single part can be purchased separately. I've talked to a couple of TDI parts companies and idparts.com told me within a year he should have a replaceable wastegate actuator for the factory turbos. He's the one who told me to try this method and so far so good!:nana2: