Place the corn syrup in a saucepan and bring to a boil over high heat. Reduce the heat to medium and add the sugar one third at a time, stirring after each addition with a silicone spatula until the sugar is completely moistened.
Increase the heat to medium high and continue stirring until the sugar has dissolved. Place the candy thermometer in the saucepan and continue cooking until the sugar is a rich amber color or until the temperature is 350°F/177°C.
Reduce the heat to medium and stir in the butter with a clean silicone spatula. After the butter has melted, slowly pour in the warm cream while stirring constantly. Be careful during this step because the mixture will bubble up violently. This is why it’s best to use a saucepan with high sides.
Continue to cook the caramel sauce, while constantly stirring and scraping the edges and bottom of the pan, until it reaches 248°F/120°C.
Remove the pan from the heat and stir in the salt and vanilla extract. Strain the caramel through a fine-mesh strainer into a heat-proof container.