Cut away the white portion, leaving 1/4 in. on the potato skins.
Place skins on a microwave-safe plate. Microwave, uncovered, on high for 8-10 minutes or until tender.
Combine the butter, rosemary, salt and pepper; brush over both sides of potato skins.
Grill potatoes, skin side up, uncovered, over direct medium heat for 2-3 minutes or until lightly browned. Turn potatoes and position over indirect heat; grill 2 minutes longer. Top with cheese. Cover and grill 2-3 minutes longer or until cheese is melted.