In a large, deep  saucepan, spread the sugar in an even layer and place over low to medium low heat. Watch it carefully. Once it starts to liquefy around the edges, use a rubber spatula to very gently stir it towards the center. Continue gently stirring until all of the sugar is melted, but take care not to over stir. Once the caramel reaches a deep amber color, immediately remove it from the heat.

Carefully whisk in half the cream, which will bubble and steam quite violently. Stir until the cream is thoroughly combined, then whisk in remaining cream. Stir in the salt and vanilla. If any sugar has hardened, place the saucepan over low heat and whisk until smooth. The sauce can be stored for up to 2 weeks in the refrigerator. It can be rewarmed in the microwave or in a saucepan set over low heat. Add additional cream if the sauce is too thick.