In a small heavy saucepan combine butter and sugar. Cook and stir over medium heat until butter is melted and mixture is bubbly. Remove from heat. Gradually stir about half of the hot mixture into egg yolks. Return egg yolk mixture to saucepan. Cook and stir over medium-low heat about 15 minutes or until mixture reaches 170 degrees F. Remove from heat.
Stir in rum. If necessary, stir in hot water, 1 teaspoon at a time, to make of desired consistency. Serve warm or cooled to room temperature. (If sauce thickens, stir in a little additional hot water.)