Combine the water, sugar and butter in a large saucepan and cook over high heat until light amber, about 5 minutes. Stand back as far as possible and slowly drizzle the cream into the caramel. It will bubble up and may splatter, so protect your hands with an oven mitt or towel. Add the rum and cook for 4 to 5 minutes, occasionally swirling in the sauce around the pan, until thickened and a rich golden brown.
Strain the sauce and stir in the sweetened condensed milk. Store in a sealed container. This sauce will keep for 2 weeks in the refrigerator or 3 months in the freezer.