Add the sugar to a heavy sauce pain.
Turn the heat to just above medium and allow the sugar to begin to melt. This may take 10+ minutes. Watch carefully as it will burn easily.
When the sugar starts to melt, begin stirring constantly to prevent burning.
The sugar will clump up but just keep stirring until all of the sugar and clumps have melted. If the color darkens too much or too quickly then turn down the heat. If any sugar clumps refuse to dissolve then continue to the next step and they can be removed later.
Whisk in the room temperature butter, one tablespoon at a time until fully incorporated.
Add the room temperature heavy cream (be very careful as the caramel may bubble and splatter at this point) and stir until the cream is fully incorporated.
Remove from the heat and then stir in the sea salt.
If any sugar clumps remain you can pour the sauce through a fine mesh sieve to remove the sugar clumps. Careful as it is VERY hot.