1 cup butter
1 cup firmly packed brown sugar
3/4 cup white sugar
2 cups vanilla ice cream, softened
10 cups boiling water, or more as needed
2 cups rum
1 teaspoon ground nutmeg, or as needed
Combine butter, brown sugar, and white sugar in a 2-quart saucepan. Cook over medium heat, stirring occasionally, until mixture comes to a boil and sugars dissolve, 6 to 8 minutes.
Mix hot butter mixture into ice cream in a large bowl.
Fill each mug with 3/4 cup boiling water, 1/4 cup ice cream mixture, and 2 tablespoons rum. Sprinkle nutmeg on top.