1. Combine sugar, brown sugar and butter in a 2-quart saucepan. Cook over low heat, stirring occasionally, until butter is melted (6-8 min).
2. Combine cooked mixture with ice-cream in a large mixing bowl, and beat at medium speed, scraping bowl often until smooth (1-2 min). Store refrigerated up to 2 weeks or frozen up to one month.
3. For each serving, fill one-quarter of a mug with mixture, add one ounce rum and three-quarters of a cup of boiling water. Sprinkle with nutmeg.