Brakes can be a pain in the ***. First off, is the sound only coming from one wheel as opposed to all four? The problem is more than likely the brake shims. Typically when brake shims are not lubricated properly they make a lot of small annoying noises when you slightly press the pedal, but when you really get on the brake pedal these noises stop because the vibration on the brake shims is halted due to pressure. The vibration is harmless, just really REALLY annoying! And you should not need to turn your rotors, as the problem is most likely unrelated.
First thing you need to do is find out where the noise is coming from and then open the brake caliper up to see if the brake shims are on the brake pads as well as checking the condition of the pads to make sure it isn't worn down. If you have brake shims, then put a small touch of copper grease or disc caliper brake lube (don't use anything else) where the piston contacts the back of the shim. Also apply lube to the back of the shim on the other side of the caliper. Put lube on metal contact points as well but try to avoid getting the lube on the rotor.
I would try that. If that doesn't work, you can try a brake bedding procedure or Brake Quiet that might help. Otherwise, it might be worth it to invest in a nice rotor/pad combo. AM has a nice one for all 4 corners for 400 bucks.
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2012 Mustang GT Premium
Michelin AS/3 Sport Tires
Eibach Adjustable Anti-Roll Sway bars
Eibach Pro-Kit Shocks/Struts w/ Springs