Grease an 11 by 7-inch flameproof baking dish with the butter and set aside.
Position 1 oven rack in the middle position and 1 in the top position and preheat the oven to 400 degrees F.
Place the cauliflower in a small glass bowl, stalk end up. Use a paring knife to remove the lower leaves. Trim the curds off of the stem, keeping them as intact as possible. Try to keep the size uniformly large and make as few cuts as possible. Discard the leaves and stem. Cover tightly with plastic wrap and microwave on high for 4 minutes. Rest, still covered in plastic, for another 4 minutes. Uncover and rest for 4 to 5 more minutes while preparing the rest of the dish.
Combine 4 ounces of the cheese, the bread crumbs, egg, salt, mustard, paprika, black pepper, and cayenne in a large mixing bowl. When 1 minute remains on the cauliflower rest period, microwave the cream on high for 30 seconds. Add the cream to the bowl with the cheese mixture and stir to combine.
Using your hands and a tea towel if the cauliflower is still hot, rub the large florets between your hands to break up the curds. Add the curds to the cream mixture and stir until the cheese is thoroughly melted and combined.
Spread the cauliflower mixture in the prepared baking dish, place on the middle rack, and bake for 20 minutes. Remove the baking dish and turn the broiler to high. Sprinkle the remaining 1/2 ounce cheese atop the cauliflower. Place on the top rack and broil until the top is bubbly and appropriately brown, 6 to 8 minutes. Rest 10 minutes before serving.