In a heavy-bottomed medium saucepan with tall enough sides to accommodate the mixture when it starts bubbling, combine the sugar and water. Heat over medium-low heat until the sugar dissolves, stirring occasionally.
Increase the heat to medium-high and bring mixture to a boil without stirring. Using caution, use a wet pastry brush or damp paper towel to wipe down any crystals that are clinging to the sides of the saucepan. Failure to remove them could result in a grainy sauce. Boil until the mixture is a deep amber color, about 5 to 6 minutes.
Remove the pan from the heat, and using caution, whisk in the cream. The mixture will bubble up vigorously.
Add the vanilla and optional rum. It will bubble again.
Stir in the butter and salt to taste; or omit salt for regular caramel sauce. If using table salt rather than Kosher salt, add less because it’s finer-grained and 1 teaspoon of table salt is much saltier tasting than 1 teaspoon of Kosher salt.
Transfer caramel to a glass or heatproof jar with a lid. Caramel sauce will keep airtight for many months in the refrigerator.