In a heavy-bottom saucepan, combine the sugar, corn syrup, and water over medium-low heat. Heat the mixture until the sugar melts. Reduce the heat to low so that it’s just barely simmering and watch closely, but don’t stir. The mixture will take about 15 to 20 minutes to turn amber brown.
Meanwhile, heat the heavy cream in a small saucepan over medium-low heat or in the microwave. When the sugar mixture is amber brown, remove it from the heat and add the cream and butter, stirring constantly until the mixture is syrupy and smooth. Stir in the vanilla extract and season to taste with the salt. The caramel sauce will keep, covered, in the refrigerator for up to 2 weeks.