Pull the husk away from the ears without detaching it. Remove the silk. Pull the husks back up around the cobs and use a small piece of husk to tie and hold in place at the end.
Pour water, white wine, and the Garlic Herb Rub into a bucket and whisk well to combine.
Place the husk-jacketed cobs upright in the bucket and weight them with a plate to submerge in the marinade. If more liquid is needed to cover, add water. Soak overnight.
Prepare the butter by combining it with the cheese, salt, garlic, and pepper in a bowl and stirring vigorously to mix well. Set aside.
Preheat the grill to medium, 350ºF. Place the marinated cobs on the grill. Grill for 15 to 18 minutes, turning occasionally. Husks will become quite dark but will pull back easily to reveal the succulent cobs, which should then be brushed liberally with the Parmigiano butter.
Arrange cobs on a platter using the pulled-back husks as handles. Serve with salt and more of the cheese butter on the side.