For sauce: In a heavy small saucepan, bring the 1/3 cup brown sugar, whipping cream, butter and corn syrup to boiling over medium-high heat, whisking occasionally; reduce heat to medium. Boil gently, uncovered, for 2 minutes more. Remove from heat. Stir in vanilla and sea salt. Cool to room temperature before serving, or chill for up to 24 hours and rewarm in the microwave on 50 percent power (medium) for 1 1/2 to 2 minutes before serving, stirring twice.