Noisy brakes

I have a loud grinding noise coming from the front brakes when I start out in the morning when the car is cold. This noise only persists at the low speeds. When the car is warmed up the noise usually doesn’t manifest itself. Has anyone else come across this noise? It is sporadic and the mechanic has not been able to duplicate it.

If there was rain, dew or other moisture the night before the brake rotors can form a thin layer of rust.
This gets wiped away after a few stops.