I was going to post about this very problem last month.

I've had this "shudder" happen at least 8 times, and only in cold weather after leaving the car parked over night. The shudders occured while the engine was trying to turn over about 10 seconds after I hit the ON switch. Here's a significant observation I made... Every time I got the "shudder" effect, it was during the following situation:

1) Hit on switch.
2) Shift into reverse and lightly press gas (4 sec. after on switch).
3) As I'm backing out of my spot in reverse, I lightly hit the brakes to slow my speed. (10 sec. after on switch)
4) The ICE attempts to start up at this point. I'm still moving backwards, but with the brakes lightly pushed. This is when I always got the shudder.

To me, it feels like the engine RPM isn't high enough when the fuel starts to flow and the engine is struggling to start (while under load).

Did anyone else notice this with their car?