I'm having this same problem and wanted to bump the thread in case anyone figured it out. I have a 2011 WRX (18,000 miles) and I've been dealing with it for about a month now. It doesn't happen consistently, so when I took it to the dealer to have it fixed under warranty, they couldn't recreate it.
Just to throw in a few more details: it'll happen regardless of whether the engine is cold or hot. It only happens on startup and will go away after a while. Like the OP, it only happens when I turn the wheel to the left. The sound is a high-pitched metal-on-metal grinding sound---almost like the front brake pad wear indicators are grinding on the rotors.
Thanks for the help...it's driving me nuts.