Combine the heavy cream, corn syrup, butter and salt in a saucepan. Bring to a simmer over medium heat, whisking; remove from the heat.
Sprinkle the sugar evenly in a large skillet. Cook over medium heat, undisturbed, until the sugar melts and starts caramelizing, about 5 minutes. Continue cooking, swirling the pan (but not stirring) until the caramel is dark amber, 10 to 15 more minutes.
Remove from the heat and add the warm cream mixture. Return to medium heat and bring to a simmer; cook, whisking, until smooth, about 7 minutes. Stir in the vanilla. Let cool slightly before serving. To store, let cool completely, then cover and refrigerate up to 2 weeks; reheat before serving.