In a heavy bottomed sauce pan, heat the sugar on medium low heat, stirring periodically, until its completely melted. The sugar will start to form clumps before melting slowly. Be patient and keep an eye on it to make sure it does not burn. As the sugar melts, increase the frequency of your stirring.
Once melted, remove from heat immediately and stir in the butter. The mixture will violently bubble. (Don't worry. This is just the hot sugar reacting to the room temperature butter.)
Pour in the heavy cream and sea salt. Stir until completely combined.
Pour into small bowl or cup and allow to cool completely before using. The caramel will continue to thicken during this time.