Pour the sugar into a medium (3 quart) pot. Carefully pour the water over the sugar, trying not to let any of the sugar ride up the sides of the pot. Carefully stir, just to hydrate all the sugar. If any sugar crystals ride up the sides of the pot, use a pastry brush dipped in water and run it along the sides of the pot without allowing the bottom of the pastry brush to touch the mixture. This will cause any sugar crystals to fall into the rest of the mixture.
On a medium-high heat, cook the sugar mixture. Swirl the pot or stir occasionally, using the wet pastry brush to wipe any sugar crystals that run up the sides of the pot. Once the mixture starts to boil, do not stir the mixture again. Just carefully swirl the pot. Cook until amber/light brown in color. It will go from light brown to burnt quickly, so pay close attention.
As soon as the caramel is cooked, turn the flame off and carefully and slowly, with a wooden spoon, stir in the heavy cream, just a little at a time. The entire mixture will bubble up violently (so be careful and add the cream in small batches) and the caramel may seize. On medium heat, heat the mixture, stirring frequently, until the caramel is melted and the entire mixture is combined and smooth and just comes to a simmer. Add the salt, vanilla and butter, stirring until the butter is melted and fully combined. Allow to cool to room temperature.
Caramel sauce can be stored in an airtight container in the refrigerator for up to two weeks. To use from the refrigerator, microwave it at 10 second intervals until you reach a runny consistency.