Combine apricots and water to cover in a heavy saucepan. Bring to a boil. Reduce heat; cover and simmer 30 minutes. Drain apricots, reserving 1/2 cup liquid.
Place drained apricots in container of an electric blender, and process until smooth. Return pureed apricots to saucepan; stir in sugar, butter, and reserved apricot liquid. Cook over low heat, stirring constantly, until mixture comes to a boil. Remove from heat, and stir in brandy. Serve sauce warm.