Boil sugar, water, corn syrup, and salt in a saucepan over medium-high heat, swirling occasionally, but not stirring. Cook until caramel is the color of iced tea, about 10 minutes. Watch it closely! It takes some time to start turning golden brown, but once it does, it can go from perfect to burnt very quickly.
Remove saucepan from the heat and add heavy cream, whisk to combine. It will foam up and and steam, so be careful! Whisk in butter and vanilla.
Transfer to a bowl or a jar to cool completely. It will thicken quite a bit as it cools. Store in fridge for 1-2 weeks.
If desired, stir in one tablespoon of rum or bourbon at the same time as the cream.
To reheat: Heat in saucepan over medium-low heat until warm or in microwave at 50% power in 45 second intervals, stirring well each time.