Weatherproofing Below Windows

Not sure what its called, but the cavity from below the window sill to the floor. In my b’stone there is wood paneling in this area. One panel popped out and now we can see why our upstairs is so hard to heat in the winter…next to no insulation between the paneling and the brick.

Looking for advice on what type of insulation is best (green materials preferred) and what type of craftsman to hire for the job in order to maintain the delicate woodwork.