In a medium heavy-bottomed saucepan, combine the butter, sugar, salt and cream. Melt over low heat while stirring slowly and gently. Once all ingredients are melted, increase the heat to medium and bring the mixture to a boil. Boil for 10 minutes without stirring. Watch the heat closely, if it seems as though the mixture might be burning on the bottom (which can often happen if you are using a pan that isn't heavy-bottomed), reduce the heat as needed.
Remove the caramel sauce from the heat and carefully stir in the vanilla (stirring vigorously at this point and/or scraping down the sides can cause the caramel sauce to develop a grainy texture). Use immediately or let the sauce cool a bit before pouring into a container to refrigerate. The sauce can be refrigerated for several weeks.