In a Dutch oven, combine the first seven ingredients. Cook, stirring constantly, over medium-low heat until the caramels are melted and mixture is smooth (do not boil). Reduce heat to low.
With an electric hand mixer on medium speed, beat in vanilla; continue beating for 5 minutes. Beat on high for 2 minutes. Remove from the heat and cool for 30 minutes (sauce will thicken as it cools). Pour into glass or plastic food storage containers; refrigerate. Serve warm or cold.