Add the sugar to a medium sized saucepan set over medium heat. Stir occasionally until the sugar begins to melt and caramelize, then stir constantly until the sugar is completely melted, caramelized, and smooth.
Add in the butter and whisk until the mixture is smooth.
Take the mixture off of the heat, and slowly whisk in the heavy cream until it is completely incorporated into the caramel. Whisk in the salt and vanilla.
Transfer the caramel into a heat-safe container and set it in the fridge to thicken up.