What's the mileage on the TT? The VVT, or variable valve timing, can get gummed up by too long between oil changes, and a rough idle is the first symptom. There are measuring blocks in VAGCOM that will show the VVT values...I've got the particulars on my other computer, will post them, if you like.
Next time you change the oil, put a can of engine flush in a warm engine and follow the can's instructions on how long to run the engine before draining the oil. I used a LiquiMoly flush and it did the trick for me.