Combine butter, brown sugar, and confectioners' sugar in a large coffee mug; stir the mixture together with a fork until well combined. Pour in the rum, add the ice cream and cinnamon, and fill the remainder of the mug with simmering water. Mix the drink with the fork until the ice cream and butter have melted together to make a creamy topping. Sprinkle with a dash of nutmeg, and serve.
