In a heavy bottomed pot (I use copper), combine the sugar and water
Heat over medium heat until sugar is dissolved, stir to combine
Bring the sugar and water to a boil, stirring occasionally as needed to ensure the caramel browns evenly. Continue cooking until the sugar turns a deep golden brown caramel color. Do not take off the heat too soon or your caramel will be runny. It needs to brown.
Once brown, remove from the heat immediately and carefully add the butter, stir.
Once the butter is mixed in completely, add in the heavy cream and stir until it is incorporated. The caramel may thicken and appear lumpy/clumpy but continue to stir and it should go smooth again.
Add in the Rum (as much as you feel necessary, 1-2 Tbsp)
Add in the vanilla and salt, stir to combine
Let the sauce cool for a few minutes then transfer to a jar or other storage container.
Caramel can be stored in the refrigerator for up to 2 weeks.