When ready to cook, set grill temperature to 450˚ and preheat, lid closed, for 15 minutes.
Brush cauliflower with olive oil and season liberally with salt and pepper.
Put cauliflower in a cast iron skillet, place directly on the grill grate and cook for 45 minutes, until golden brown and the center is tender.
While cauliflower is cooking, combine melted butter, parmesan, garlic and parsley in a small bowl.
During the last 20 minutes of cooking, baste cauliflower with the melted butter mixture.
Remove cauliflower from the grill and top with extra parmesan and parsley if desired.