Preheat the oven to 375 degrees F. Slice off and reserve the top 1 1/2 inches of the pumpkin. Scoop out the seeds and stringy pulp. Rub the inside of the pumpkin with the butter, then rub with 1 tablespoon brown sugar and a pinch of salt.
Combine the rice, evaporated milk, molasses, vanilla, cinnamon, the remaining 3 tablespoons brown sugar and a pinch of salt in a small saucepan and bring to a boil, stirring occasionally.
Put the pumpkin in a baking dish and fill the pumpkin with the rice mixture. Cover with the pumpkin top and add 1 inch of boiling water to the baking dish. Cover loosely with foil and bake until the pumpkin is tender and the rice pudding is thick, about 2 hours. Scrape the pumpkin flesh and stir into the rice pudding; sprinkle with brown sugar.