Make the Basic Caramel according to the directions. Immediately remove the pan from the heat and very slowly and carefully add the cream (the mixture will bubble up furiously), stirring with a spatula or wooden spoon until smooth. If there are any hardened bits of caramel sticking to the bottom of the pan, set the pan over medium-low heat and stir until they are dissolved. Add the butter and stir until melted. Stir in the vanilla extract.
If not using immediately, cool to room temperature, cover, and refrigerate for up to 5 days. Serve warm or cool. To reheat, microwave on high, stirring every 20 seconds until hot, or heat in a small pan over medium-low heat, stirring until hot.