Preheat grill to 350-400 degrees F. Remove most of the husks on the corn and leave the innermost layer intact. Pull them back just enough to remove the silks, then place back over the corn.
Place corn on preheated grill. Cook, turning once or twice until kernels are bright yellow, 15-20 minutes.
In the meantime: place butter and garlic in a small heat-safe bowl. Microwave until butter is melted, 10-15 seconds.
Remove remaining husks and brush the corn kernels with melted garlic butter while still hot. Sprinkle with Parmesan cheese and parsley.