This is quite common.
One theory is that the inlet side gets gunked up and the carbon deposits cause the 'hiccups'. The TFSI suffers with these deposits more than a lot of engines due to the direct injection.
You can get the deposits cleaned out - the only way of doing it properly is doing it manually. Walnut blasting is an effective means. I know Alex at AKS Tuning offers this service and he's done a few now.
However, it could be a number of other things causing it. Misfire (plugs/coils), injectors etc. It'd be worth getting a scan done to rule as much out as you can, although a slight misfire might not log a code.
I'm in a similar boat. Mine has always done it but it seems to be worse these days on a cold start, before the revs drop down to a steady 700-800rpm. Jolting, shaking, popping from the exhaust, it's all a bit rough. Once the revs settle it's all nice and smooth, with only the occasional tiny pop from the exhaust that doesn't transmit any vibration. Until recently the car behaved flawlessly under load, with Stage 2 hardware on a Stage 1 (R-Tech) map, but since I got the map updated to Stage 2 a few weeks ago I've had problems under load at full boost - fuel cuts, limp mode, and misfires at about 4k.
I'm going to approach these problems first, and see if it has any effect on the dodgy idle. I'm hoping an uprated fuel pump (Loba purchased and ready for fitting) and new coil packs sorts the problems I've had after getting the map updated. If not it could be MAF, injectors, LPFP... pretty much anything. It had new spark plugs along with the major service a few weeks ago so I can at least rule those out, in theory.
Let us know how you get on.