Heat cream in a small saucepan over low. In a medium saucepan, stir together sugar, corn syrup, and 1/3 cup water; cook over medium-high, without stirring, until mixture is dark amber in color, about 15 minutes.
Remove from heat; carefully pour in cream (mixture may splatter) and stir until smooth. Reduce heat to medium and cook until a candy thermometer reads 238 degrees, about 2 minutes.
Pour mixture into a medium bowl; stir in salt. Let cool about 15 minutes, then stir in butter, 1 tablespoon at a time. Let cool completely.