Preheat grill to medium-high heat.
In a large bowl, toss together the apple wedges, melted butter, brown sugar, cinnamon, and nutmeg.
Place apple wedges on preheated grill and cook for 4 minutes per side, or until just tender.
In a small bowl, mix together the remaining melted butter, brown sugar, and spices.
Brush the glaze over the apples as they are grilling.
Serve hot with a sprinkle of extra cinnamon, if desired.