Combine butter, brown sugar and sugar in 2-quart saucepan. Cook over low heat, stirring occasionally, 6-8 minutes or until butter is melted.
Combine cooked mixture with ice cream in large bowl; beat at medium speed, scraping bowl often, until smooth. Store refrigerated up to 2 weeks or frozen up to 1 month.
To serve, fill mug with 1/4 cup mixture, about 1 ounce rum or 1/4 teaspoon rum extract and 3/4 cup boiling water; sprinkle with nutmeg.