Heat oven to 375 degrees. Bake potatoes on sheet pan until very soft, about 75 minutes. When cool enough to handle, peel and mash.

In a small saucepan, heat coconut milk with curry paste over low heat. Mix coconut milk mixture, half the sugar, half the butter and salt into potatoes. Keep warm until ready to serve, or cover and refrigerate up to two days.

At least 30 minutes before serving, heat oven to 425 degrees. Put potatoes in a baking dish, cover with foil and bake 20 minutes. Uncover, dot with remaining butter and sugar and broil until brown and crusty, checking often to prevent scorching.