Place sugar and corn syrup in a 4-5 quart kettle and place over medium-high heat.
2 cups granulated sugar, 2 tbsp light corn syrup
Let sugar begin to melt. The sugar will liquefy around the edge of the kettle. Begin to stir constantly to ensure the sugar melts evenly.
Stir until the sugar is completely melted and dark amber in color.
Remove from the heat.
Slowly stir in heavy cream in small amounts. The caramel will bubble vigorously, but continue adding cream until it is incorporated and the caramel is smooth.
1 cup heavy cream
Add the vanilla extract and rum, if using.
2 tsp vanilla extract, 1 tbsp rum
Add in cold butter and stir slowly to bring down the temperature of the caramel. Stir until completely smooth.
4 tbsp unsalted butter
Pour into an airtight jar and store in the refrigerator.
Video
Notes
Caramel will harden when it's in the refrigerator. To use, bring to room temperature or heat slowly in the microwave.