Does this happen just when you are letting out the clutch? Shudder when you hit the go-pedal? Does it quit when you let off the pedal?
If this is what is happening, I'd check your inner CV joints.
How many miles on the car?
There is a possibility that the torque mount (aka dogbone) could be causing this - a general vibration felt as shudder through the steering.
I just replace the dogbone on my Golf. The unit that was replaced seemed OK, but afterward, it was much smoother on initial takeoff.
And a different car I (temporarily) own, a 2001 Jetta, had a shudder when you pushed on the go-pedal that disappeared when the CV joints were swapped side to side.
I would be greatly surprised if your '06 has as many miles as either of the cars I just mentioned above, however, as one is at 180k miles and the other at 237k miles. And mileage would be the prime factor in either CV joints or dogbone giving up. Manufacturing defects do happen however, so it would be good to check these items.
Other possibilities aren't any fun either. The other ones I think of are DMF flywheel troubles and something loose in the front end gear such as a tie rod, ball joint, strut bearing, or other suspension components.