I drilled 1".
At first I left the cavity around the shank. The trim cover on the service side and the washer/nut on the inside will stop any air movement. But, the faucets will get cold (mine did at least).
Later I decided to pack some foam window seal inside the cavity. I think it just caused the shank to stay warmer so I pulled it back out.
No air moves but, somehow the lack of filler allows the faucets and shanks to chill and I think this is better.